113. The Hubble tension is a late Universe or local phenomenon

/ Elena / 1 Comment

Preface by P.Kroupa: This is a guest post by Dr. Indranil Banik, a postdoc at the University of Portsmouth, who is studying solutions to the Hubble tension. An interesting aspect of his problem comes from “the tension” being the automatic result of the formation and continued evolution of the local “KBC void“, a void we are in (not at its center: Mazurenko et al. 2024, 2025) and which spans about 600 Mpc. I learned about this huge under-density of matter at a conference in Durham, was it around 2013? Ryan Keenan gave a presentation about his work and I referred to it in my 2015 invited review (about cosmological problems), then calling it the “Karachentsev-Keenan underdensity” since the depth and size of this observed underdensity clashes massively with the ΛCDM model of structure formation. I asked a diploma student to study the dynamical and kinematical effects of such an underdensity, but this work did not proceed well. Much later, Moritz Haslbauer joined the SPODYR group in Bonn in about 2019 as a PhD student, and Indranil joined as an Alexander von Humboldt Fellow in 2018, and so this problem could be tackled by two very talented young scientists. While a Hubble tension could have been predicted from the continuing dynamical evolution of the underdensity already in 2013, Haslbauer, Banik and me (2020) showed that (1) this observed KBC void is inconsistent (at more than 5σ confidence) with the ΛCDM model, (2) that such underdensities can evolve in MOND-based cosmological models, and (3) that the observed depth and expanse of the KBC void accounts perfectly for the by then discovered Hubble tension. The reason for this is elementarily simple: galaxies in the void fall towards its sides like water flows downhill. From my perspective, the problem of the Hubble tension is solved locally (i.e. we have a “late-time” solution), and I keep being amazed to witness how the relevant scientific community keeps discussing it (see the list of talks here for example) in terms of complicated many-parameter models of time-evolving dark energy, dark energy–dark matter couplings that are meta- if not borderline-physics as they are never verifiable, while at the same time entirely ignoring the void solution. Indranil Banik is a unique, and also sharp and brave young scientist who keeps studying the Hubble tension in terms of the KBC void, looking at this problem from various observational directions and angles and using diverse empirical tracers. Here he provides an account of his most recent work on this matter.

Guest post by Dr. Indranil Banik:

One of the most pressing and widely known issues in cosmology is the Hubble tension, a statistically significant mismatch between the rate at which redshift rises with distance in the local Universe and the predicted rate in the ΛCDM standard cosmological paradigm calibrated using observations of the cosmic microwave background (CMB). There is now a broad community consensus that this Hubble tension is real (H0DN Collaboration 2025). I have previously written about it on DMC 106. The tension is currently >7σ. To give some context, the scientific gold standard for a discovery is 5σ. The famous Eddington eclipse expedition in 1919 ruled out the Newtonian prediction for deflection of starlight by the Sun at 7σ (Dyson, Eddington & Davis 1920). Evidently, the Newtonian prediction of 0.88″ at the Solar limb is too small. In contrast, the prediction of Einstein’s theory of General Relativity is twice as much (1.75″). This larger prediction was only 1.2σ discrepant with the observations (1.93″ ± 0.15″). Therefore, ignoring the Hubble tension nowadays would be similar to continuing to support the Newtonian prediction for light deflection after this was falsified by photographs taken during the 1919 total Solar eclipse, as illustrated in Figure 1.

Figure 1. Results of the Eddington eclipse expedition, showing the deflection angle of starlight as a function of the inverse of the angular separation of the star from the Sun during the total Solar eclipse of May 1919. Plotted in this way, both Newton and Einstein predict a linear relation because the deflection is expected to be larger for rays of starlight that pass closer to the Sun. Deflections are shown in seconds of arc, while separations from the Sun are shown in minutes of arc. The red line shows the Newtonian prediction, while the steeper blue line shows the prediction of Einstein. Observations are shown as black points, which represent stars in the Hyades Cluster. The alignment of the Sun and Moon with this dense star cluster allowed for one of the most famous hypothesis tests ever conducted. Its high statistical significance is similar to that of the Hubble tension. Adapted from Dyson, Eddington & Davis (1920).

I have previously advocated (see the publication Haslbauer, Banik & Kroupa 2020) that outflow from a large local underdensity or void could solve the Hubble tension as it would inflate the redshifts of distant objects, giving the misleading appearance of a high Hubble constant H0. This model correctly predicted baryon acoustic oscillation (BAO) data far better than ΛCDM. However, in this post, I will assume that the Universe is homogeneous on the scales relevant to local measurements of H0 through the local redshift gradient. In other words, I will assume that the Hubble tension is at the background level.

The main question with this assumption is whether the new physics required to solve the Hubble tension arises primarily before recombination, or arises mostly at late times. If my assumption of homogeneity is not correct but is still assumed anyway, then the data would favour a late Universe solution. This is because the distortions to redshifts caused by a local void would decay in the more distant universe, where the apparent expansion history would line up with the ΛCDM model. One can view this as a decay of the Hubble tension with redshift, which I previously discussed in some detail (DMC98).

The studies I will describe test if ΛCDM is valid in the late Universe. If it is, the Hubble tension is probably due to new physics prior to recombination, which if included correctly would cause us to infer higher H0 from the CMB. This is a tempting idea, but is it right? My recent short review (with Nick Samaras, then a PhD student with Pavel Kroupa in Prague) tries to check this by using several late Universe probes to infer H0 and the matter density parameter ΩM, the fraction of the cosmic critical density that is presently in the matter component. Apart from the local redshift gradient, these probes are at intermediate redshifts (z > 0.2) where a local void would have little effect. In an early time solution to the Hubble tension, all these probes should line up because there is no physics beyond ΛCDM at late times. The only discrepant probe should be the narrow parameter range inferred from the CMB using ΛCDM, due to the alleged new physics at early times skewing the results.

We can check this prediction using Figure 2. The yellow band shows the local redshift gradient, while the thin grey ellipse with central white dot shows the CMB constraint assuming ΛCDM. The discrepancy between the two is clear: this is the Hubble tension. The red band shows constraints on the shape of the expansion history from uncalibrated Type Ia supernovae (SNe Ia) and BAO datasets, though the results are similar with only BAO. Uncalibrated in this context means there is no assumption on the value of the SN Ia absolute magnitude or on rd, the comoving length of the BAO ruler. This conservative approach is still very powerful. The blue band shows the age of the Universe based on the oldest Galactic stars, assuming they took 200 Myr to form. The green band uses the matter power spectrum, which has a characteristic turnover scale from the epoch when matter and radiation had the same energy density. This occurred when the universe was about 3× smaller than at recombination and 7× younger. If new physics is introduced that primarily comes in shortly before recombination (as occurs in typical early time solutions), the physics around the epoch of matter-radiation equality is not much affected. This makes the turnover scale in the matter power spectrum a useful additional constraint, since it is unlikely for new physics at early times to bias our inference of H0 and ΩM from both the CMB and the turnover scale in the matter power spectrum by precisely the same amount.

Figure 2. Constraints on the Hubble and matter density parameters from various lines of evidence, as indicated in the legend and discussed in the text. The dark blue band shows the age constraint assuming a gap of 200 Myr after the Big Bang for the first stars to form, while the light blue band allows a factor of 2 uncertainty in this formation time. Notice the local redshift gradient is the outlier, not the CMB. Note that h ≡ H / 100(km/s/Mpc). Reproduced from figure 1 of Banik & Samaras (2025).

It is clear from Figure 2 that the discrepant observation is the yellow band showing the local redshift gradient. Remarkably, the CMB inference in ΛCDM is quite consistent with all the other probes mentioned above. This does not tally with an early time solution to the Hubble tension. Instead, the results clearly show that the new physics must be at quite low redshift so that only the local redshift gradient is anomalous. One way to think of this is that if the Hubble tension has an early time solution, it persists out to high redshift. The expansion rate would be 9% faster than expected at any redshift for pretty much the whole of cosmic history. This would reduce the predicted age of the Universe from the classical 13.8 Gyr down to 13.8/1.09 = 12.7 Gyr. However, many Galactic stars and globular clusters are older, as reviewed at some length in our paper due to referee concerns. This invalidates purely early time solutions to the Hubble tension.

Figure 3. Similar to Figure 2, but with different studies used to obtain each non-CMB constraint. The green shaded band now collapses to the black contour, though this is now more model-dependent. Even so, apart from it and the CMB, the other constraints do not rely on the validity of ΛCDM at early times. Reproduced from figure 2 of Banik & Samaras (2025).

To check this important result, we prepared another version of Figure 2 where all constraints are updated apart from the CMB. The results are shown in Figure 3. The main visual difference is that the green constraint from the large-scale matter power spectrum now collapses to the black contour. The other constraints remain similarly accurate and barely move. It is still the case that the CMB is consistent with all considered constraints except the local redshift gradient, which is now obtained from a different study using quite different methods. Naturally the referees asked in some detail about these constraints, so you will have to read the paper if you want to know more about some of the subtleties involved, e.g. why Freedman erroneously claimed a low H0. I know many researchers have reservations about the use of SNe Ia in cosmology, but you can exclude them if you like and you would still get a steep local redshift gradient incompatible with the ΛCDM-based CMB value, for instance using Cepheids alone (Stiskalek et al. 2025).

We also explain in our review that the Hubble tension cannot be due to inaccurate measurements of the 0.001% level CMB anisotropies. The Hubble tension can only be solved on the CMB side consistently with ΛCDM through a substantial change to the CMB monopole temperature, or through changes to several other interlocking lines of evidence. Therefore, it is unlikely that more accurate observations of the CMB can remove the Hubble tension faced by ΛCDM. Where they could help is by constraining early time solutions that leave specific signatures on the CMB, now that we have observations covering the first ten acoustic peaks in the CMB power spectrum (Camphuis et al. 2025). However, there are major problems with the general idea of solving the Hubble tension through new physics prior to recombination, as discussed below.

Testing if the Hubble tension is solely a late Universe effect

There are broadly two ways in which a study could show that the Hubble tension should be solved primarily or entirely through new physics that affects the late Universe:

1) Assume ΛCDM physics at early times and work inwards to low redshift with a flexible expansion rate history. Without using the local redshift gradient as a constraint, predict its value. Success in this context means this prediction agrees with the consensus local value of H0 ≈\approx 74 km/s/Mpc, because that would mean no tension between the predicted and observed H0.

2) Assume the consensus local H0, then work outwards with a flexible expansion history without using constraints that assume ΛCDM at early times. In particular, rd must not be fixed to the ΛCDM value. Success in this context means the expansion history asymptotically approaches the ΛCDM prediction calibrated to the CMB.

Working inwards from high redshift

Jia et al. (2025) follow the first approach. They use BAO + uncalibrated SNe Ia, by which I mean their absolute magnitude is left free. This is important because without knowing the absolute magnitude, the analysis does not know the local redshift gradient. It can therefore predict this (you cannot predict something that you use as an observational constraint to fix your model parameters). Although the SNe Ia are uncalibrated, the BAO data are calibrated assuming the standard value for rd.

The main point of the analysis is that the dark energy equation of state is assumed to be constant within narrow redshift bins, but a step-like change is allowed between bins. This makes the expansion history fairly flexible. The authors use the expansion history to draw a curve of H0(z), assuming ΛCDM to extrapolate the reconstructed H(z) curve to z=0. In ΛCDM, all such extrapolations would lead to the same H0 regardless of which redshift you start at. So any trend in H0(z) is a sign that ΛCDM is not valid in the late Universe. Essentially, departures of H0(z) from the CMB-derived value of 67 km/s/Mpc measure how much the Hubble parameter at that redshift departs from the ΛCDM expectation calibrated to the CMB.

Figure 4. Inferred H0(z) curve using a flexible expansion history constrained by uncalibrated SNe Ia from different catalogues (different panels) and BAO data from DESI DR2, calibrated assuming rd has the standard ΛCDM value of 147 comoving Mpc. Since the local redshift gradient is not used as a constraint, the analysis is able to predict its value. Remarkably, this prediction matches the observed value. Reproduced from figure 5 of Jia et al. (2025).

The results are shown in Figure 4. Even though SNe Ia are uncalibrated, the model remarkably predicts that H0 is consistent with the consensus local value given its uncertainties! This is evident with either the Pantheon+ sample or the more recent Dark Energy Survey Year 5 (DES Y5) sample. In the latter case, the SNe Ia are too distant to be calibrated directly through the Leavitt Law of Cepheid variables (Leavitt 1912). In the Pantheon+ case, absolute calibration is possible. If using just the Pantheon+ sample, the results at low redshift favour a high H0, as is well known. But the Pantheon+ only column of table 2 in Jia et al. (2025) shows that the data in the highest redshift bin yield a lower H0 of 69.8 ±\pm 1.4 km/s/Mpc, in plausible agreement with the CMB-derived value. Therefore, even SNe Ia alone have a declining H0(z) trend.

The same is true with the BAO data, since low redshift BAO data points imply a lower distance to fixed redshift than predicted in ΛCDM. This implies a steeper redshift gradient, or higher H0. However, the higher redshift BAO points are in line with ΛCDM (see figure 4 of Banik & Kalaitzidis 2025). Since both BAO and SNe Ia show a descending H0(z) trend, it makes sense that combining them leads to the same conclusion. The important result is that the trend is sufficient to resolve the Hubble tension.

The ability to recover the high local H0 assuming ΛCDM at early times without using the local redshift gradient as a constraint is indeed remarkable. It likely explains why the title boasted of “resolving the Hubble tension”. This of course overstates the importance of the paper, since showing that the Hubble tension should be solved in the late Universe does not solve the problem. But it does significantly constrain possible solutions.

Working outwards from low redshift

López-Hernández & De-Santiago (2025) follow the second approach I outlined above. They also construct a curve of H0(z), but they use a broader range of constraints. They minimise controversy by using uncalibrated SNe Ia and uncalibrated BAO, which means rd is left as a free parameter. To get a constraint on the local redshift gradient, they use megamasers, which provide purely geometric distances (Pesce et al. 2020). They also use cosmic chronometers, which constrain the slope of the time-redshift relation. These constraints are chosen to be as uncontroversial as possible, but the precision is somewhat lower as a result.

Figure 5. Similar to Figure 4, but now neither SNe Ia nor BAO data are calibrated. To obtain absolute H0 values, the expansion history is also constrained using cosmic chronometers and the purely geometric local redshift gradient measurement using megamasers. Results are shown separately for three different SNe Ia catalogues. The Hubble tension is evident in the lowest redshift bin. Remarkably, the results in all other bins are far more in line with the CMB value assuming ΛCDM at all times, a value that is not used as a constraint at any stage. The Hubble tension is thus absent in this analysis outside the lowest redshift bin. Reproduced from figure 1 of López-Hernández & De-Santiago (2025).

The results are shown in Figure 5. Although the freedom in rd means there is no assumption of ΛCDM at early times, the recovered H0(z) curve quickly declines from the high local value down to the CMB-derived value. In fact, apart from the lowest redshift bin, the results are far more in line with the CMB value. This is true regardless of which SNe Ia dataset is considered, since the authors obtain similar results using three of the most commonly considered datasets. Note these SNe Ia datasets are not independent and hence cannot be combined. I would suggest looking at only the DES Y5 sample because it is a large recent sample collected using the same instrument, minimising issues related to calibrating fluxes on different telescopes.

Conclusion

Both Jia et al. (2025) and López-Hernández & De-Santiago (2025) agree that the Hubble tension is likely a late Universe phenomenon. This was also the result found by Pantos et al. (2026). Indeed, it is by now clear that the Hubble tension is largely a mismatch between the local redshift gradient and other estimates of H0 from data at higher redshift, not just the CMB. One such example is γ-ray attenuation, which gives a value of 62.4+4.1-3.9 km/s/Mpc (Domínguez et al. 2024). This is just about consistent with the standard CMB value, but well below the consensus local redshift gradient. The technique relies on significant path lengths for the γ-rays, so it lacks sensitivity at the low redshifts where the Hubble tension arises. Very few studies in recent years have claimed to find evidence for a 9% level Hubble tension using only data at z > 0.3, but many find the opposite.

Although we discussed it in our review , cosmologists rarely consider the ages of the oldest Galactic stars and globular clusters. This is another powerful argument that the solution to the Hubble tension is not through new physics prior to recombination. I think cosmology nowadays is a quest to obtain two numbers: H0 and AU, the age of the Universe. If we know the true background expansion rate of the Universe and its age, that would clarify a great deal, including whether we are in a local void and whether the Hubble tension should be solved through new physics prior to recombination. I am currently working on refining the estimated age of the oldest star in a large sample, so look out for my results on this! I am currently constructing the article now that detailed calculations are complete and the figures are ready.

The balance of evidence now strongly favours late Universe solutions to the Hubble tension. These would have little effect on the age of the Universe, which therefore cannot easily discriminate between different scenarios (Nájera et al. 2026). I am considering ways to distinguish the local void scenario from solutions at the background level. If this crucial distinction is left unresolved, theorists will have little clarity whether to modify the Friedmann equations or the growth of structure. I therefore think that an important goal for cosmology should be to narrow down which of these options is correct, and then construct theoretical models that achieve such an adjustment.

It is still unclear what exactly is causing the Hubble tension. But the latest results provide important clues that will help theorists focus on the most promising solutions. The accelerating rate of progress gives me great hope that the Hubble tension can perhaps be resolved in the not too distant future.

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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112. The meaning of the cosmic microwave background (CMB) for cosmology, and the role early galaxies have in this matter

/ Prof. Dr. Pavel Kroupa / 1 Comment

This contribution documents my presentation of the meaning of the cosmic microwave background (CMB) for cosmology and the role that massive galaxies forming at high redshift play in the physics of the CMB. The presentation was invited by Dr. Jaroslav Haas at the Astronomical Institute of Charles University in Prague, and was delivered by me on December 10th, 2025. It was recorded by Matthew Bell from London, but only with his documentary in mind, so it cannot be replayed with sufficiently clean slides. Given the response of the audience I agreed to record this lecture again from my office to make it available to whomever might be interested to learn of the scientific arguments and the line of reasoning.

I encourage absolutely everybody to redo the calculations, this being necessary because the conclusions are of great importance for our understanding of cosmology.

In this context I do want to emphasise that up until some two years ago (e.g. see DMC103) I had no reason to doubt the standard interpretation of the CMB as it being the relic radiation from the Hot Big Bang. What drove me to start questioning the current canon are the two simple facts that (1) the standard LCDM or LWDM models do not describe cosmological reality by cosmologically-relevant dark matter particles having been ruled out by the Chandrasekhar dynamical friction test (see DMC99 and our most recent publication Hernandez & Kroupa 2025), and (2) no alternative non-dark-matter based model (such as MOND-based models) has been until now able to convincingly reproduce the observed Universe. It took me sometime to understand that the currently published Planck power spectra of the CMB can only be valid for the dark-matter based standard model of cosmology, which however, are not describing physical reality (since dark matter has been falsified to exist using the Chandrasekhar dynamical friction test). So then what are the Planck power spectra? And what is the CMB?

The recording of the presentation can be found on the “spodyr spodyr” channel and also here:

The slides:

10Dec25_Praha_onCMBDownload

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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111. The funding of dark matter research

/ Prof. Dr. Pavel Kroupa / 2 Comments

On a previous occasion (DMC73) I had made a rough estimate into the funding volume spent on dark matter research. David Merritt pointed out this web site to me today (19.Nov.2025):

dark matter funding.

On this page (by https://simonallzen.quarto.pub) we read “I sourced all the available public funding data for dark matter projects from various regions around the world. The data is visualized below, segmented by region: Europe, North America, United Kingdom, and Japan.” Details are not given and would constitute a major volume of information, so it is not clear if the assessed funding accounts for the relevant accelerator-based searches (i.e. the actual expensive running of the machine), the expensive super-computing times used for generating dark-matter-based results and the salaries of the involved people (engineers, programmers, scientists).

According to the data in the link,

  • USA spent nearly 4×109 (4 billion) US$ in the time 1987-2025, i.e. 105 million per year. 
  • EU spent 300 million Euro on dark matter research in the time 2014-1025, i.e. 30 million per year.
  • Canada spent 28 million C$ in the time 2014-2025, i.e. 2.5 million C$ per year.
  • UK spent 47 million pounds in the time 2006-2025, i.e. 2.4 million pounds per year.

Thus we see, according to the above assessment, a volume of roughly 130 million US$ per year being expended on dark matter research in only these four regions/countries (e.g. S.Korea, India, China, Russia, Iran, Australia, Switzerland are not counted).

It is fascinating, how so much tax payer money is being used to look for something that does not exist. That dark matter particles do not exist is actually well proven scientifically (with more than 5σ confidence) – see this most recent review: “Dynamical Friction Constraints on the Dark Matter Hypothesis Across Astronomical Scales” by X.Hernandez & Pavel Kroupa (2025). But accepting this would mean that many scientists would not be able to keep applying for tax payer’s money for searches for dark matter, so it is better to just ignore, or even better, try to shut-down or even expel the scientists publishing tests telling us there is no dark matter (see The Winnie-the-Pooh adventure in DMC90). By claiming to the public to not know there is no dark matter, the responsible scientists keep a funding machinery in the loop:

new experiment/calculation (=a) 
==> no evidence for dark matter / problems in matching to observed systems (=b) 
==> new experiment/calculation (=a) 
==> no evidence for dark matter/problems in matching to observed systems (=b) 
==> a ==> b ==> a ==> b ==> a ==> b ==> a ==> b ...
==> ad infinitum.  
At the end of time a humongous amount of research money is being wasted with no other than null results

We are thus in a a truly most remarkable period in the history of humanity: Since the Renaissance science did not experience this type of madness, which perhaps is mirrored by the quite rapid and truly fascinating transformation of western societies into interesting “modern” forms increasingly based on a very powerful “religion”.

In comparison, the MOND Research Programme (read David Merritt’s “A Philosophical Approach to MOND: Assessing the Milgromian Research Program in Cosmology“, see also DMC55) uses much less tax-payer money: Since no experiments have (to my knowledge) been funded explicitly with Milgromian dynamics in mind, we merely need to estimate the salaries of some ten researchers world wide that are active on this topic: ten times 50000 US$ (taking 50000 US$ to be the average salary, including some professors, heroic postdocs and the odd extremely brave PhD student) makes 0.5 million US$ per year.

The discovery by Mordehai Milgrom of “Milgrom’s critical acceleration” a0 (reported in the seminal research publications 1983a, 1983b, 1983c) constitutes one of the very greatest scientific discoveries of the 20th century. This discovery has lead to completely new predictions of previously unknown galaxy-dynamics phenomena (e.g. BTFR, RAR as well as asymmetric tidal tails of open star clusters, see the above “A Philosophical Approach to MOND”) which have all been verified to an astonishingly excellent degree. Basically, the discovery of a0 constitutes the discovery of a (probably quantum-related) process of the vacuum related to gravitation. In contrast, the dark-matter models have lead to complete and total disagreement with basically any measurement ever made (see e.g. The many tensions with dark-matter based models and implications on the nature of the Universe).

Understanding the origin of a0 is the holy grail of modern physics. Success in finding this holy grail is likely to open a completely new understanding of space, time and matter and their interrelated evolution. That the scientific community is largely ignoring a0 is a scandal, a tragedy of modern science, a crime against the tax payer, an explicit demonstration that the scientific method has been abandoned by the vast majority of researchers working in cosmology and galaxies.

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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110. Newton and Einstein on Dark Matter

/ Prof. Dr. Pavel Kroupa / 6 Comments

Guest blog by Prof. Dr. Xavier Hernandez

Our current established theory of gravity is General Relativity as presented by Albert Einstein in 1915. This theory by construction reduces to Newton’s law of gravity whenever typical velocities are substantially below the speed of light. As this condition is met in all the astronomical systems discussed here, considering theoretical predictions, both theories will be referred to indistinctly. In the case of spiral galaxies, the theoretical prediction was for rotation speeds which, much as happens in the Solar
System, would decrease with increasing distance from their centres, once beyond an inner raising region. This inner raise was indeed detected in the 1960s and 1970s, but in a formal falsification of the theory, beyond this initial raising region, rotation curves have now been firmly established to remain flat at constant values. Rather than recognise this falsification, the standard answer to this stark gravitational anomaly has been to postulate the existence of huge dominant halos of hypothetical “Dark Matter” particles responsible for providing the missing mass and hence the missing force, which observed rotation curves require under a classical interpretation of gravity. These halos must comprise upwards of 90% of the mass budget of galaxies. Despite decades of intensive searches for a direct detection of these supposedly abundant particles, all experiments have returned only null results, discarding one candidate dark matter particle after another, as the scale and range of the detection technology grows to increasingly impressive sensitivity values decade after decade.

This being one of the principal mysteries of modern day science, one cannot help but wonder at what Newton and Einstein themselves would have thought of the problem. While a conclusive answer in this respect is of course impossible, interesting clues on what the two proponents of our theories of gravity might have made of this can be ascertained from their thoughts as found in the historical record.

In 1713 Newton finished the second edition to his Principia, which includes an Editor’s Preface by Roger Cotes, who in modern terms we could term as Newton’s research assistant. It is accepted that this preface was written in close collaboration with Newton himself, and closely reflects Newton’s philosophical approach to science. A recent modern English translation of this preface can be found in e.g. The Mathematical Principles of Natural Philosophy .

Portrait of Isaac Newton, 1689, in his forties. From Wikipedia.

In the third paragraph of this preface, we find a description of certain types of scientists:

“…they are right to progress from the simpler to the more complex, provided that they do not endow these fundamental aspects of particles with more than nature herself endowed. But when they take it upon themselves to ascribe whatever unknown shapes and sizes they wish to the parts, with unknown structures and motions, and indeed to hypothesise certain occult fluids that permeate the pores of bodies very freely, endowed with an overwhelming subtlety, and stirred by occult forces, they are now floating off into dreamland, and have lost contact with reality; a reality that will be sought in vain with false conjectures, and that can scarcely be investigated by even the most certain observations. It must be said of those who base their speculations on hypotheses, even if they then proceed very precisely according to mechanical laws, that they have constructed a fable, which, however elegant and beautiful,
remains a fable.”

It is tempting to read this as a prescient derision of galactic dark halos as currently envisioned, with density profiles, abundance matching prescriptions and 3D geometries to be adjusted at will so that resulting rotation curves can be matched to any desired accuracy, in the total absence of any direct detection or direct empirical evidence of the existence of any dark (occult?) component, which is described as being all around us and constantly going through the Earth (and even ourselves!) without leaving any detectable trace or effect, other than the required gravitational signal on galactic rotation curves. Even if scientific methods are used to build an edifice upon a fantastical hypothesis, what is being constructed is nothing other than an elegant fable.

What Newton was criticising here was not of course the current dark matter hypothesis, but in fact the prevalent explanation of the time to the motions of planets. Then, it was accepted that planets were carried about the Sun on “Cartesian Vortices”, eddies of some yet undetected fluid which was assumed to fill the Solar System and which in analogy to the stable eddies which sometimes carry with them floating bits and pieces on a water current, would transport the planets on their elliptical paths. While the object of Newton’s ridicule was not our modern dark matter, his aversion to explanations requiring postulating a dominant causal entity which by construction can always be hypothesised as sufficiently undetectable to evade direct empirical restrictions at any given time, is obvious.

Some 230 years later, Mexican physicist Carlos Graef Fernandez was on a research visit to Princeton University. Graef was at the time one of the leading proponents of an alternative theory of gravity put forward by the renowned US physicist George David Birkhoff. This theory was consistent with special relativity and allowed an accurate description of planetary motions, while being much simpler than the quite mathematically cumbersome General Theory of Relativity of Einstein, at the expense of requiring (again….) the introduction of an all pervasive and undetectable fluid to fill the universe, Birkhoff’s perfect fluid, with properties calibrated to get observed orbits right.

Left: Albert Einstein in 1921 (Wikimedia). Right: Einstein’s home in Princeton (Wikimedia).

Graef was invited by Einstein to discuss this theory and the two met in Einstein’s home in December of 1944. Following the death of Albert Einstein, Graef presented a detailed account of that interview in the April 1956 issue of American Scientist, Vol.44, No.2, pages 204-211, under the title “My tilt with Albert Einstein”. This can be found in e.g.: My Tilt with Albert Einstein.

Three sections of this account are highly relevant. At the beginning of the account Graef tells us:

“A maid ushered me to the library. Einstein greeted me with a smile and a piercing but friendly stare. After exchange of courtesies, Einstein genially remarked:

‘I think the principal difference between Birkhoff’s point of view and mine lies in what we consider to be the scientific explanation of a physical system. Now what is your opinion in this matter, Graef?’

‘Well, let us consider a concrete example, say the Solar System’ I answered. ‘I think a person who has a set of formulae which enables him to predict accurately the future of the Solar System has completely
explained that system.’

By this, if you are so good as to follow me, I meant that one who fully understands the Solar System can unerringly predict the positions of the Moon, Mars, Venus, Jupiter, Saturn and the other planets, at any given hour of any future date.

Einstein could not conceal his impatience. ‘Do you really think that what you claim is all there is to an explanation?’

‘Yes. An explanation for us is nothing but an order of formulae which empowers one to predict the future.’

Einstein vehemently disagreed. ‘The set of formulae, which for you is all there is to an explanation, has to be consistent with the philosophy of nature in order to be a true explanation. Otherwise it is only a convenient device for predicting the future of a system, but does not give a real insight into its nature.’ “

Here we see that for Einstein, describing a physical system, with whichever degree of accuracy, is fundamentally distinct to understanding it, a point which Graef evidently missed. Mayan astronomers were capable to “unerringly predict the positions of the Moon, Mars, Venus, Jupiter, Saturn (…), at any given hour of any future date” together with Solar eclipses and even transits of Venus, to greater accuracy than their observational uncertainties, merely through centuries of carefully inferring the regularities of the Solar System, without ever reaching any understanding of the system treated whatsoever. They were utterly incapable of predicting the orbit of a comet, even though it follows the same physical prescriptions as planets, which are only apparent once one actually understands the system. Similarly, the more refined Ptolomean models with the Earth at the centre of the Solar System were more accurate representations of the relative positions of the planets than the early Copernican ones with the Sun at the centre, once enough epicycles and deferents had been meticulously adjusted. Given sufficient freedom to tune hierarchical clustering merging histories and feedback recipes, any real galaxy can be matched to an accurate analogue found within the millions of systems appearing in large cosmological simulations, affording however little understanding of the fundamentals of the problem. Parameter fitting exercises rarely reveal the deep underlying physics of a system.

The conversation proceeded to:

“Therefore it was with lively curiosity that I asked: ‘Prof. Einstein, how exactly does this philosophy of nature rule out, in your opinion, Birkhoff’s Theory of Gravitation as an explanation of the Solar System?’

Said Einstein: ‘For Newton, the fundamental cause for the curved motions of the planets was the Sun itself. The great mass of the Sun, in the center of the system, attracts celestial bodies in the vicinity toward itself. Thus the presence of a mass in space is the cause of the force that urges the planets on their courses.’

‘But contemporary physics,’ he went on, ‘has abandoned this point of view. Today we consider the force as primary, as more fundamental. The physicist can measure this force directly, as he does on Earth. Contemporary science prefers to consider those physical entities, the planets, as fundamental; as causes which can be observed and measured directly. And it prefers to think of entities which cannot be measured or observed directly, like the Sun, as derived or secondary.’

Einstein paused to let his words sink in, then: ‘Thus you see, Graef, a theory built to explain the Solar System has to start with the field of forces, the planets. The mass of the Sun itself is a derived quantity because, as I have already remarked, it cannot be observed or measured directly. The primary quantities, the planets, are the forces which all point toward a center. We consider that at that point, the center, there is a singular something which we call ‘mass of the Sun.’

‘This mass, you understand, Graef, is obtained by calculating it from the planets – the measured forces.’

‘But in Birkhoff’s Theory,’ Einstein shook his head, ‘the fundamental cause for gravitation is a liquid. His point of view is a step backward. He goes back to an unobservable and unmeasurable quantity for the cause of gravitation.’ Again he shook his leonine head in disapproval, then, with a smile, added: ‘Whereas in my theory the mass of the Sun is derived and calculated from the observed and measurable motion of
the planets.'”

Einstein understood that using planetary orbits and his General Relativity Theory implies the presence of a certain mass at a certain point in space. This point coincides with the position of the Sun, whose existence is plain to all. Indeed the actual value of the required mass of the Sun coincides with stellar interior physics theory, completing the detailed independent confirmation of the causal entity which Einstein requires to explain planetary orbits, and satisfying him that an understanding of the problem had been reached, as it is now universally agreed. It is explicit that to Albert Einstein, ascribing the cause of gravitation to “an unobservable and unmeasurable quantity” constituted a very disappointing “step backward”.

The texts described above clearly lead to a plausible answer to the question poised at the start: both Isaac Newton and Albert Einstein would quite possibly have been fairly repulsed by the idea of an undetectable and dominant Dark Matter component as the determinant causal entity behind the formation, evolution and structure of galaxies. Regarding the present dark matter hypothesis, note that Chandrasekhar dynamical friction constraints now afford a formal falsification of dark matter particles as the cause of astronomical gravitational anomalies, as recently reported in DMC99. Indeed, the validity of classical gravity at low accelerations, upon which the dark matter hypothesis is based, has been shown to break down through the analysis of wide binary orbits, as summarised in DMC95, and through the force field around open star clusters as mapped out by their leaving stars (paper1, paper2)

The American Scientist article ends with an editor’s note putting the preceding interview into context. This includes making it clear that Birkhoff’s theory of gravitation was all but discarded at the time; indeed it now counts as barely a footnote in the history of mid 20th century physics. This final note also includes a comment by Professor Peter G. Bergmann as follows:

“As for the story itself, I believe than non-physicist readers should know that Einstein himself never considered his own theories as immutable or final. It is quite true that the General Theory of Relativity is not consistent with the special theory any more than the special theory is with Newton’s mechanics – each of these theories discards, in a sense, the conceptual framework of its predecessor. But each new theory also contains its predecessor as a limiting, simplified version; after all, it must be capable of yielding the correct results of the earlier theory as well as extend the range of our understanding. During the last thirty-five years of his life Einstein himself was searching for an improvement of physical theory, beyond the General Theory of Relativity. Probably he has proposed (and discarded after examination) a greater number of so-called unified theories than any worker in the field.

We are all aware of the preliminary character of the General Theory of Relativity, as in fact of any physical theory”

This comment illustrates a degree of openness towards exploring new theories which is presently often hard to find. It is remarkable that a view which is now often treated as almost heretical in General Relativity Physics and cosmology groups, the preliminary character of General Relativity, which is not immutable or final, was indeed the accepted frame of mind not only of physicists in general 70 years ago, but indeed was shared by Einstein himself! That new observations which falsify an established theory should lead to the rejection of such theories is in principle the standard scientific expectation, rather than a miscreant deviation to be stamped out.

The author, Xavier Hernandez, in the restaurant Los Danzantes in Coyoacan with Pavel Kroupa during the latter’s visit at UNAM in early October 2025.

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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109. Recent progress on dark matter, gravitation and the CMB

/ Prof. Dr. Pavel Kroupa / 1 Comment

The Archive Trust for Research in Mathematical Sciences and Philosophy, Bristol, is organising a series of lectures on Quantum Foundations, Particle Physics, and Unification of Forces, referred to as OSMU . The hosts are Tejinder P. Singh and Michael Wright.  The lectures and discussions are recoded and published on YouTube. The links to the event, to the programme and to the recordings can be found below.

Added on 25th October 2025: Roger Penrose & Friends : The Archive Trust for Research

The recordings of talks in mathematical sciences and philosophy are documented on The Archive Trust for Research.

The next OSMU lecture will be given by Pavel Kroupa on October 17th on the topic: 

Recent progress on dark matter, gravitation and the CMB

Abstract: I will explain that the Chandrasekhar dynamical friction test using the Large and Small Magellanic Clouds (LMC, SMC, respectively) rejects the existence of cold or warm dark matter particles as the LMC and SMC would have merged a long time ago while we know they are on a stable orbit about each other with an orbital time of less than a Gyr. Therefore non-relativistic gravitation must be effectively Milgromian. This is confirmed by the recent detection of a significantly larger number of evaporated stars ahead of four open star clusters than behind them, an asymmetry which falsified Newtonian gravitation with 8 sigma confidence but is in rather stunning agreement with the calculations of the evaporation made with Milgromian gravitation. Given that the two pillars of modern cosmology are therewith destroyed (no dark matter and non-relativistic gravitation is effectively Milgromian rather than Newtonian), it is of no surprise that issues arise even with the CMB being the photosphere of a hot Big Bang. Massive elliptical galaxies had to synthesise to super-Solar metal abundances in less than a Gyr requiring a top-heavy galaxy-wide stellar IMF to supply a sufficient number of massive stars for this nuclear synthesis. Taking the known elliptical galaxies back to the time they formed at a redshift near 18 implies a photon density created through these nuclear reactions that competes with that supposedly produced in the surface of last scattering near a redshift of 1100. This foreground was unknown until now and raises very serious concerns in terms of the origin of the full CMB. 

The recorded talk plus discussion is available on YouTube (added on 25th October 2025): Recent progress on dark matter, gravitation and the CMB

The previous, very similar colloquium, held at UNAM on 1st of October, is available on YouTube (added on 25th October 2025): Recent progress on dark matter, gravitation and the CMB.

The slides are available here (added on 17th October 2025):

Recent progress on dark matter, gravitation and the CMBDownload

Links:

Zoom Link for all talks is:

https://us06web.zoom.us/j/89956931861?pwd=YkN4bUg0NE1STFlRd0MwY0NUVjcwdz09

Meeting ID: 899 5693 1861
Passcode: 451794

The OSMU2025 schedule is available at:

Click to access OSMU2025.pdf

The video recordings of OSMU2025 lectures are available at: OSMU2025

The video recordings of OSMU2024 lectures are available at OSMU2024

The video recordings of OSMU2023 lectures are available at OSMU2023

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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108. The tidal stability of dwarf galaxies as a critical challenge to cold dark matter

/ Prof. Dr. Pavel Kroupa / 1 Comment

The Archive Trust for Research in Mathematical Sciences and Philosophy, Bristol, is organising a series of lectures on Quantum Foundations, Particle Physics, and Unification of Forces, referred to as OSMU . The hosts are Tejinder P. Singh and Michael Wright.  The links to the event and the programme can be found below.

The next OSMU talk will be given by Indranil Banik on Friday, October 3, 2025 at 3 pm UK time, on the topic:

The tidal stability of dwarf galaxies as a critical challenge to cold dark matter

Abstract: Dwarf galaxies are small, faint galaxies that are usually found in galaxy clusters or near larger galaxies. This makes them potentially susceptible to the gravitational effect of these structures, which can disrupt their morphological appearance. The Fornax Deep Survey dwarf galaxy catalog provides us with information about several properties of the dwarfs in the 20 Mpc distant Fornax cluster, including the observed level of morphological disturbance of the dwarfs. This can be used to compare if their theoretically calculated tidal susceptibility matches observations. Dwarfs are not expected to be very susceptible to tides in the standard model (ΛCDM) where galaxies follow Newtonian gravity and have cold dark matter halos, since these halos enhance their self-gravity, which makes the dwarfs more resilient to the effect of gravitational tides. However, Milgromian dynamics (MOND) predicts that dwarfs are more easily disturbed by tides despite the boost to gravity provided by MOND. The reason is that this enhancement mimics the effect of a dark matter halo for an isolated dwarf, but the enhancement to gravity gets significantly damped once the gravitational field of a larger object dominates over that of the dwarf (this is known as the external field effect, which is unique to MOND). In this talk, we compare the observed morphological disturbance of 353 Fornax dwarfs with their expected tidal susceptibility in ΛCDM and MOND using different types of analyses. Our results show that the MOND prediction for the level of disturbance of the Fornax dwarfs matches the observations much better than the ΛCDM prediction, which is in significant tension with the observational data (MNRAS, 515, 2981). Similar conclusions follow from our recent analysis of eight classical Galactic satellites, whose proximity allows for deeper observations and more accurate knowledge of their 3D orbit. Several satellites show clear signs of tidal disturbance, which can be understood in MOND given their perigalacticon distance, but all analysed satellites should be quite immune to tides in ΛCDM. Our results can be thought of as an extension of the core-cusp problem to unprecedentedly low stellar masses, where baryonic feedback effects should be weak, implying a more fundamental problem with the cold dark matter hypothesis. Note: the slides were prepared by the lead author of both works, Elena Asencio.

Reference:
https://doi.org/10.1093/mnras/stac1765

The recorded talk plus discussion is available on YouTube (added on 25th October 2025): The tidal stability of Fornax cluster dwarf galaxies in Newtonian and Milgromian dynamics

The slides of the talk are here: (added 23.10.2025)

OSMUDownload

Links:

Zoom Link for all talks is:

https://us06web.zoom.us/j/89956931861?pwd=YkN4bUg0NE1STFlRd0MwY0NUVjcwdz09

Meeting ID: 899 5693 1861
Passcode: 451794

The OSMU2025 schedule is available at:

Click to access OSMU2025.pdf

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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107. Do the stellar streams of the Milky Way point to a past Milky Way-Andromeda interaction?

/ Elena / 2 Comments

by Elena Asencio

The stellar streams of the Milky Way are disrupted remnants of dwarf galaxies and star clusters that are still orbiting our Galaxy. Several studies (Odenkirchen et al. 2003, Erkal et al. 2016) have pointed out that stars in stellar streams approximately follow the same orbit as their parent object. This means that the orbits of stellar streams can be used to infer their origin. A useful parameter to evaluate the properties of an orbit is the orbital pole (see Figure 1).

Figure 1: Image representing a stellar stream orbiting a galaxy. The orbital pole (white arrow) is the vector perpendicular to the orbital plane of an object, and is obtained as the vector product of the stream’s orbital velocity and the stream’s distance to the Galactic centre. Credit: image adapted from NASA / JPL-Caltech / R. Hurt, SSC & Caltech.

Kroupa et al. (2005) found that the Milky Way dwarf satellite galaxies could be fitted to a disk and that their orbital poles agreed remarkably well. Years later, Pawlowski et al. (2012) confirmed this for a larger dwarf galaxy sample and showed that several Milky Way globular clusters and stellar streams also had similar orbital poles to those of the satellite galaxies. The authors named the structure formed by all the objects with similar orbital poles the “Vast Polar Structure” (VPOS). The similarities in the orbits of all these Milky Way substructures suggests that they might have a correlated origin. Pawlowski et al. (2012) proposed a scenario in which the Milky Way and Andromeda had a past encounter billions of years ago, which led to the formation of tidal tails around these galaxies. Objects formed within the same tidal tail (e.g. dwarf galaxies, globular clusters, stellar streams streams, etc.) have very similar orbits. Therefore this would provide a satisfactory explanation for the similarities in the orbital poles of most Milky Way substructures, as well as the planar configuration of the satellite galaxies.

An important caveat of this scenario is that it does not work in the ΛCDM standard model. The reason for this is that, if the Milky Way dwarf galaxies had formed in tidal tails, they would be dark matter free (the velocity dispersion of the dark matter particles is too high for them to cluster on tidal tails). We know that this is not possible because these dwarf galaxies have very high velocity dispersions that can only be explained with dark matter in this framework. Additionally, in ΛCDM, the Milky Way and Andromeda would be surrounded by a dark matter halo, and the dynamical friction of their dark matter halos would have caused these galaxies to merge during the interaction.

This scenario does however work in alternative frameworks like Milgromian dynamics (MOND, Zhao, Famaey & Kroupa 2013). In MOND, the dynamics of galaxies are explained through a modification of Newtonian gravity in the regime of low accelerations (< 1.2 × 10-10 m/s²). Therefore, in this model, the high velocity dispersions of the satellite galaxies can be explained through the MONDian boost to gravity, without having to resort to dark matter. Also, without dark matter halos, Andromeda and Milky Way would not merge during the interaction.

In other words, if most of the Milky Way substructures have a correlated origin, MOND (and MOND-like models) would then be the most natural framework with which to understand the formation of the Milky Way substructures. Because of this, verifying the correlated origin hypothesis can have important implications in our understanding of structure formation and galactic dynamics.

The study of Asencio, Kroupa & Thies (2025) explores the orbital pole distribution of one of the most recent stellar stream catalogues (galstreams) with the aim of testing whether this large stream sample (91 independent streams) still has a preferred orbital pole direction, similar to that of the satellite galaxies (green cross in figure 2). For this, the authors obtained the number of stream poles which where at a distance < 36.87º from the orbital pole of the satellite plane (green circle in figure 2, this covers 20% of the considered parameter space) and classified them as VPOS members. Then, using Bernoulli statistics, they obtained the probability (P) that a homogeneous distribution would give the same fraction of VPOS members as observed. So that high P values indicate consistency of the observed pole distribution with a homogeneous distribution and low P values indicate consistency with an inhomogeneous distribution favouring the VPOS area.

Figure 2: Distribution of the orbital poles of the MW streams included in the galstreams catalogue. Since only one orbital sense is considered, just one half (120º to 300º) of the longitudinal range is shown. The nominal orbital poles for each stream are represented by the large coloured points. Their uncertainty is shown by the point clouds of the same colour. The green cross marks the position of the observed orbital pole direction of the satellite plane (Pawlowski et al. 2015) and the green circle surrounding it represents the threshold of the VPOS membership area.

When considering the full stream sample, the authors found that the fraction of VPOS members is 15/91, which corresponds to a P value of 0.83 ± 0.09. In other words, the pole distribution is highly consistent with a homogeneous distribution. This seems to challenge the hypothesis of a common origin for most Milky Way substructures. However, the authors also noted that, as they removed streams closer and closer to the Galactic centre, the fraction of VPOS members would progressively increase. That is, for a sample with streams at Galactocentric distance (d) > 10 kpc, the fraction of VPOS members became 13/55 and, for a sample at d > 15 kpc, the fraction became 10/37. Additionally, the authors pointed out that there appears to be a lack of orbital poles near the equator (see Figure 2). This means that there seems to be a lack of streams with polar or quasi-polar orbits with respect to other orbital directions.

The increasing trend of VPOS members with increasing Galactocentric distance can be explained if the stream poles were originally clustered in the VPOS area but were displaced by precession effects. The gravitational torque of the Milky Way centre (precession) could have easily affected the orbital pole orientation of the MW streams by causing a displacement in their longitudinal direction (the horizontal direction in Figure 2). Since precession is stronger for streams closer to the Milky Way centre, the streams with low Galactocentric distance would have been the most displaced. Precession would also explain the lack of orbital poles with quasi-polar orbits. This is because stars within a stream with different latitude positions will precess at different rates, and this will cause the stream to widen over time and make it harder to observe. The widening effect is stronger for streams with polar orbits, while the displacement effect is stronger for streams with equatorial orbits (Erkal et al. 2016).

Equation 2 in Ibata et al. (2001) provides an analytic description of the angular displacement experienced by the orbital poles due to precession as a function of time. Using this equation, the authors of the present paper backtraced the positions of the streams’ orbital poles to 6.6 billion years ago (a time shortly after the Milky Way-Andromeda interaction, according to hydrodynamical simulations of the encounter). This increased the total sample fraction of VPOS members to 23/91, which reduced the P value to 0.13 ± 0.04. That is, once the effect of precession is taken into account, the orbital pole distribution becomes more inhomogeneous with a preference for clustering towards the VPOS region, which is what would be expected if most of these streams had a correlated origin.

The previous method can be a useful way to estimate the positions of the stream orbital poles if they hadn’t been affected by precession. But in order to appreciate the pole clustering around the VPOS directly from observations, one would need to select streams that are sufficiently far away from the Galactic center in order to avoid precession effects. By using hydrodynamical simulations of a Milky Way-Andromeda interaction (Banik et al. 2022), the authors were able to estimate the Galactocentric distances at which the resulting tidal debris would present a pole preference in the VPOS direction (in Figure 3 it can be appreciated how the clustering of the poles towards the VPOS increases with increasing Galactocentric distance).

Figure 3: Tidal debris pole distribution at different Galactocentric distance (d) cuts taken from the present-day Banik et al. (2022) simulation of a Milky Way-Andromeda interaction. For a better comparison with the observed sample, it was also assumed that the simulated substructures are all orbiting with the same orbital sense.

From their analysis, they inferred that samples including substructures at a distance 50 kpc < d < 150 kpc should already present an appreciable degree of clustering. Unfortunately, the current observable stream sample only includes streams at d < 100 kpc (with about 70% of the streams being at d < 20 kpc), so no VPOS preference can be determined directly from the orbital poles with high statistical confidence. However, other objects like star clusters and dwarf galaxies can be more easily observed at higher Galactocentric distances (due to their higher mass and luminosity), and their orbital poles already display the expected VPOS preference (Pawlowski et al. 2015).

In summary, the current data on stellar streams already shows favourable results in support of the VPOS hypothesis — that is, the hypothesis that most Milky Way substructures are part of a single structure with a common origin. Still, it will be necessary to include stellar streams at high Galactocentric distances in the sample in order to confirm this with full certainty. Verifying this hypothesis can have a great impact in our understanding of structure formation in the Universe, given that the only scenario that can currently explain the formation of such super-structure is incompatible with the standard model of cosmology. Recent surveys such as Gaia are expected to provide information on fainter, more distant streams, so the confirmation of this hypothesis might not be too far off.

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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106. Insights on cosmological tensions from the CosmoVerse Napoli workshop

/ Elena / 6 Comments

Guest post by Dr. Indranil Banik

I recently attended a three day conference on various tensions facing cosmology, including especially the Hubble tension and possible solutions to it. I will discuss talks on similar topics together in what follows. Just a quick reminder about the special issue in Galaxies on the Hubble tension that me and Harry Desmond are guest editing, where you can submit review articles and original research that looks at the problem observationally or theoretically (DMC100).

Large-scale structure

The first day focused mostly on large-scale structure. It is usually quantified in three main ways. The first is correlating positions of galaxies with the positions of other galaxies, leading to a clustering amplitude as a function of scale. The second is to correlate the shapes of galaxies with the shapes of other galaxies, yielding measurements of cosmic shear. The third is to correlate the shapes of galaxies with the positions of other galaxies, allowing measurements of galaxy-galaxy lensing in a stacked sense.

In a sign of how rapidly cosmology is evolving, the workshop was arranged when there was still a tension in S8, a measure of how clustered matter is on a scale of 8/h Mpc in the local Universe. However, there is no such tension with the latest data according to a recent study that improved nearly all aspects of the analysis (Wright et al. 2025). This means it is no longer necessary to invent exotic explanations for the S8 tension.

An interesting talk on the first day was given by Will Handley on how to quantify the tension between different datasets in the context of a model with many parameters (Handley & Lemos 2019). The basic idea is to compute the Bayesian Evidence. An example could be the tension between the cosmological parameter constraints inferred by different datasets. Some quite expensive calculations along these lines are currently underway, assessing the consistency between baryon acoustic oscillation (BAO) measurements and the anisotropies in the cosmic mircowave background (CMB), whose observed anisotropies provide strong constraints on any cosmological model by providing a way to essentially ‘listen’ to the early Universe (see DMC98).

The motion of the Sun relative to the CMB should cause sources ahead of the Sun to appear brighter, leading to a greater number of detectable sources in this direction (and vice versa). There is indeed a dipole in the number counts of radio sources above some specified flux threshold, with results fairly robust to this threshold (Wagenveld et al. 2024). The Solar velocity that one can infer from this dipole agrees fairly well with that inferred from the dipole in the CMB temperature. Various shortcomings were discussed with previous claims of an anomaly, which were not taken seriously given the latest data. Moreover, the anisotropy in source number counts should depend on the used source catalogue in a specific way if it is caused by the rest frame of the sources differing from that of the CMB, because it depends on the redshift and colour distribution of the sources and other properties. It is not clear that the observed anisotropy is best explained as a purely kinematic dipole (Wagenveld et al. 2025).

Two other anomalies in the CMB were also discussed. The first was the anomalies in the CMB on large scales, which were also discussed in some detail at the end of day 2 of the conference in Thessaloniki (DMC94). These claims are subject to the look-elsewhere effect, since the CMB is very widely studied, with many researchers on the lookout for anomalies, and a large amount of data in which to look for them. The second was a new tension discussed by Frode Hansen identified by cross-correlating the CMB with a map of nearby spiral galaxies. The CMB appears to be cooler in these regions, suggesting an enhanced Rees-Sciama effect compared to the usual expectations. The sign of the effect is opposite to the integrated Sachs-Wolfe effect, which is therefore unlikely to be the explanation. Unusually, the signal is stronger around spiral galaxies than ellipticals. This suggests some role for net rotation of the galaxy. It was suggested that magnetic fields coupled to axionic dark matter might be anomalously cooling CMB photons. If the signal is real but the distinctions between galaxy types is not, then it could be a sign that structure formation is faster than expected in ΛCDM.

Measurements of the local redshift gradient and the Hubble tension

The mornings of the second and third days focused mostly on measurements of the local redshift gradient cz’, which is often erroneously equated with H0 even though this is not defined as cz’, but rather as the time derivative of the cosmic scale factor a at the present epoch. H0 matches cz’ only in a homogeneous cosmology where redshift z only arises from changes in a over the lookback time r/c (Mazurenko, Banik & Kroupa 2025). Recent claims to obtain a low cz’ by Freedman et al. (2025) were comprehensively debunked (Riess et al. 2024). The earlier claim of consistency with the CMB-derived value involved blinding in certain aspects of the analysis. However, the choice of which galaxies to observe could easily have been tailored to get a low cz’, thereby pushing the dodgy narrative of no Hubble tension. No clear answer was given to the crucial question of how these galaxies were selected, raising the distinct possibility that they were selected in order to get a low cz’ and argue that there is no Hubble tension, something that Wendy Freedman has long been pushing despite overwhelming evidence to the contrary. No researchers on an independent payroll took this narrative seriously, mainly because there are many other teams working on measuring cz’ and they get consistent results, as shown in Figure 1 (Scolnic & Vincenzi 2023). I will describe the main techniques we discussed and a few other important ones that were missed, combining statistical and systematic errors in quadrature for simplicity.

Figure 1: The local cz’ in km/s/Mpc estimated using the distance ladder approach, showing the plethora of options for the first and second rungs beyond the traditional Cepheid-SNe Ia route. A few techniques make use of fewer or more than two rungs. Purely geometric techniques that use zero rungs are not shown here, but several are discussed in the text. Reproduced from figure 1.4 of Scolnic & Vincenzi (2023).

The gold standard is the traditional route involving Cepheids and Type Ia supernovae (SNe Ia). There are 4 anchor galaxies where the Cepheid period-metallicity-luminosity relation can be calibrated because we have trigonometric distances. Assuming the same relation holds further out, we can find the absolute magnitudes of 42 SNe Ia (47 light curves) in 37 distinct galaxies. This gives cz’ = 73.17 ± 0.86 km/s/Mpc (Breuval et al. 2024). Despite a vast effort to undermine this inconvenient measurement, no attempt has succeeded. If we instead trust this inconvenient measurement given the vast array of checks that it has passed, we find that cz’ is (8.2 ± 1.4)% higher than predicted in ΛCDM if its parameters are calibrated using the CMB anisotropies. This falsification of ΛCDM at 5.8σ confidence in a supposedly strong area for the paradigm was the main reason for having the conference.

We can replace Cepheids in the first rung of the distance ladder with the J-region of the asymptotic giant branch, with the JAGB magnitude serving as a standard candle to calibrate distances to SNe Ia host galaxies. This approach gives cz’ = 73.3 ± 2.4 km/s/Mpc (Li et al. 2025). This is a fairly new technique, with further scope for standardising the JAGB magnitude using other information like the shape of the magnitude distribution.

Instead of building the distance ladder using the traditional Cepheid-SNe route, we can use an alternative route where the tip of the red giant branch (TRGB) is used in the first rung and surface brightness fluctuations (SBF) in the second or top rung. This gives cz’ = 73.8 ± 2.4 km/s/Mpc (Jensen et al. 2025) without using either Cepheids or SNe Ia.

The top rung of the distance ladder does not have to use SNe Ia as their role can be replaced with various galaxy scaling relations, in particular the Tully-Fisher Relation (TFR) and Fundamental Plane (FP). It has recently become possible to obtain cz’ using the FP relation provided we know the distance to the Coma Cluster (Said et al. 2025). This anchor distance is indeed known very well, implying that cz’ = 76.5 ± 2.2 km/s/Mpc (Scolnic et al. 2025). The uncertainty is dominated by that in the distance to the Coma Cluster. Unlike many other techniques, the relation between this distance and the local cz’ only became clear recently, making earlier estimates immune to moral hazards regarding the Hubble tension. Moreover, the CMB-derived H0 was not known all that well until about ten years ago, so earlier distance measurements are even more immune to moral hazards. The Coma Cluster would need to be >110 Mpc away to have no Hubble tension, but this is larger than any published distance measurement since 1990. Nobody has suggested that Coma is actually 110 Mpc away, with the literature converging on about 100 Mpc. Moreover, replacing the FP relation with the TFR in the top rung gives cz’ = 76.3 ± 2.6 km/s/Mpc (Boubel et al. 2024, Scolnic et al. 2024). The FP and TFR are rather distinct because the former applies to elliptical galaxies and the latter to spiral galaxies, so it is interesting that they give such similar cz’.

It is also possible to measure cz’ using various techniques that do not rely on a distance ladder approach. An exciting recent development in this regard is the expanding photosphere method (EPM) applied to Type II SNe. Unlike SNe Ia where there is still some controversy about the underlying mechanism, SNe II are core-collapse SNe. The idea of the EPM is to apply the Stefan-Boltzmann Law to the SN remnant. To get the same apparent magnitude, we would need to place the SN further away, since the emissivity is known from the temperature. In this case, changes in the size from one day to the next would need to be larger (e.g., a 5% change in size represents a larger change if the remnant is more distant and thus larger). This is where the observed kinematics of the remnant come in. The observed line profiles can tell us about the kinematic structure of the remnant, breaking the degeneracy between explosions of different sizes at different distances with the same temperature. Alternatively, the observed kinematics tell us the actual expansion velocity of the remnant. A more distant explosion would need to have a larger remnant, so the same actual expansion velocity would lead to a proportionately smaller change in the size and thus in the apparent magnitude, affecting the light curve. In this way, detailed observations and modelling of SNe II show that cz‘ = 74.9 ± 1.9 km/s/Mpc with “no rungs attached” (Vogl et al. 2025).

Fast radio bursts (FRBs) can serve as beacons that illuminate our understanding of the Universe. The radio waves propagate through the intevening matter at a velocity that depends on the frequency, with higher energy radiation able to get through slightly faster, while lower energy radiation is more affected by electromagnetic interactions with free electrons. Since we know the baryon density of the Universe from Big Bang nucleosynthesis and expect the intergalactic medium to be largely ionised, we can deduce the distance to an FRB. In some instances, the FRB has been localised to a particular source galaxy, in which case we also know the redshift. FRBs generally lie at rather low z and give an estimated cz’ of about 75 ± 3 km/s/Mpc, depending on the model assumptions (Kalita, Bhatporia & Weltman 2025).

We can also estimate cz’ using megamasers, powerful radio sources in the central regions of galaxies. It is possible to obtain a direct trigonometric distance to a megamaser by comparing precise astrometry of the system to the acceleration, which we can observe from the rate at which the radial velocity changes. Only for one particular distance would the material near the black hole be on a Keplerian orbit, which it should be. Combining redshifts and distances to 6 megamaser galaxies out to 132 Mpc gives cz’ = 73.9 ± 3.0 km/s/Mpc (Pesce et al. 2020).

Given the above, it is interesting to ask why some researchers still believe that undetected systematics with the local cz’ measurements have caused them all to be biased upwards by about 8%. If the values from such widely different techniques had been in similarly good agreement with each other but they had clustered around 67 km/s/Mpc, would cosmologists really doubt the measurements? Of course not. In that scenario, the excellent agreement between the local measurements and the CMB value would be hailed as a remarkable success of modern cosmology. But in the actual case of a statistically significant disagreement, the local measurements must be subject to unknown systematics, a hypothesis which by definition is hard to test. In any case, if cz’ has the expected value based on the CMB in ΛCDM, it seems unlikely that the measurements would all be higher by about the same amount despite the widely different techniques involved.

The expansion history at high redshift

There was some discussion of extending the distance ladder approach using quasars and gamma-ray bursts. There were constructive discussions of how to appropriately handle Malmquist bias, the tendency for only the brightest objects to be discovered because fainter ones fall below the detection threshold. While it would be useful to constrain the expansion history at high redshift, I pointed out that the BAO results at z = 2.33 are in excellent agreement with the Planck cosmology, suggesting that there is only very limited scope for modifications to it at redshifts between 2.3 and 1090, the redshift of recombination. Alternatively, deviations in this range would need to cancel out in some sense. While that is possible and this wide redshift range should certainly be explored, it remains unclear how any deviations from the Planck cosmology in this regime might help to solve the Hubble tension consistently with the BAO data. Moreover, the dark energy component is sub-dominant at such high redshifts, so altering its equation of state (how its density changes with time) would have little impact on the expansion rate at such early times, which are dominated by matter and (eventually) radiation.

This raises the possibility of altering the matter equation of state, which could happen due to backreaction effects caused by the energy density stored in the gravitational field itself. Since gravitational potentials due to large-scale structure are quite shallow (e.g., the Local Group of galaxies is nowhere close to becoming a single black hole), backreaction effects are generally expected to be very small. It is possible that they are not, though one wonders how the S8 measurement might be explained in this case. Oliver Piattella gave a talk in which it was assumed that the matter equation of state has the standard value of zero early on, but then jumps to some other value below some redshift, which roughly speaking should correspond to when the Universe became significantly structured. When considering both the CMB anisotropies and the BAO data, the results show a worsening of the Hubble tension (Giani, Von Marttens & Piattella 2025).

This raises the more general issue that at face value, the BAO data require a faster expansion rate than in the Planck cosmology at redshifts of about 0.3 — 1 (Mukherjee & Sen 2025). These results have sometimes been interpreted as due to the dark energy density evolving with time, but they were predicted in the local void scenario assuming a background Planck cosmology, which has a constant dark energy density (Banik & Kalaitzidis 2025). Returning to homogeneous models, a faster expansion rate at intermediate redshifts needs to be compensated by a lower expansion rate at low redshifts to preserve the angular diameter distance to recombination, which is necessary to preserve the ΛCDM fit to its angular power spectrum. As a result, altering the expansion history to fit the anomalous BAO data implies H0 = 64 ± 2 km/s/Mpc, worsening the Hubble tension (Mirpoorian, Jedamzik & Pogosian 2025).

Given these difficulties, the delegates were asked about whether the Hubble tension could be solved through new physics prior to recombination or by altering its redshift. None of the forty or so delegates voted for this. The main reason was probably that despite accurate observations of the CMB anisotropies across a large range of angular scales using several instruments, there is no positive evidence for the most commonly considered proposals along these lines, which by now casts doubt on their validity (Calabrese et al. 2025, Camphuis et al. 2025). While it might be possible to solve the BAO anomalies by altering the redshift of recombination, the fact that the BAO anomalies are much smaller in percentage terms than the Hubble tension prevents a simultaneous solution to both problems, which would require altering the sound horizon at recombination by both 2% and 8% at the same time. Moreover, the age of the Universe based on the oldest Galactic stars and globular clusters agrees very well with that in the Planck cosmology (Cimatti & Moresco 2023, Valcin et al. 2025). While this approach uses absolute ages, we can also use differential ages of stellar populations at different z to constrain how rapidly z changes with time, a technique known as cosmic chronometers (CC). This technique gives H0 = 68.4 +1.0 –0.8 km/s/Mpc (Guo et al. 2025). The results are therefore consistent with the Planck cosmology, but well below the local cz’. This is not a problem as such because the CC results are at an effective redshift of about 1 and have limited sensitivity to the z < 0.15 regime typically used to measure cz’. Moreover, strong lensing time delays of SN Refsdal also give a low H0 much more in line with the Planck value (Kelly et al. 2023; Grillo et al. 2024). This is also the case with strong lensing time delays of quasars, at least once the lenses are appropriately modelled and various biases are taken into account (Li et al. 2025). In the future, spatially resolved kinematics of the lenses should give a better idea of whether the expansion history returns to the Planck cosmology at higher redshift, as suggested by various lines of evidence and used to argue in favour of a large local void (DMC98).

Future outlook

Given the strong evidence for the Hubble tension and the complete lack of confidence in solutions at early times in cosmic history, the discussions turned to solutions at late times, or locally. Several researchers were already familiar with the local void scenario, on which I recently gave a talk.
https://www.youtube.com/watch?v=vEL7VkCxkIA

The fine-tuning of our location in the void was yet again raised as an objection to the scenario, despite having been addressed earlier (Haslbauer, Banik & Kroupa 2020). A generic feature of late-time or local solutions is that there is a return to the Planck cosmology at high z. Supernova data have been used to argue against this as they apparently favour the expansion rate being 8% faster than in the Planck cosmology out to at least z = 0.5 (Kenworthy, Scolnic & Riess 2019). This could be used to set the size of the BAO ruler, since there are certainly some quite accurate BAO measurements from this redshift onwards. If the supernova results are taken at face value, the expansion rate must then have been faster than in the Planck cosmology over the vast majority of cosmic history. This would violate the CC results and the ages of old Galactic stars and stellar populations. Moreover, it would require substantial modifications to the physics prior to recombination to ensure compatibility with the observed CMB anisotropies.

Delegates did not favour this scenario. Instead, they took the only viable path forward: doubting the SNe Ia results that purportedly show no return to the Planck cosmology. Several delegates raised the issue of how SNe Ia are standardised based on their colour and stretch, a measure of the timescale over which the remnant goes from peak brightness to 1.5 magnitudes fainter. There are strong trends in the stretch and colour with redshift (Nicolas et al. 2021; Wojtak, Hjorth & Hjortlund 2023). As a result, misunderstanding of how these influence the peak absolute magnitude of SNe Ia can lead to additional trends in the reported luminosity distance with redshift — or hide an actually present trend. Further analyses of SNe Ia are necessary to assess whether they might be consistent with a return to the Planck cosmology at high redshift.

While measurements of the local cz’ seem quite secure, it would be interesting to obtain CC measurements at low z. This is because CC measurements further out are in line with the Planck cosmology (Guo et al. 2025). If CC measurements closer in show the anomaly expected from the cz’ measurements, it would be a rare instance of seeing the Hubble tension emerge within a single dataset rather than by combining datasets, which is much more vulnerable to zero-point errors in one or more of the datasets being combined. The predicted CC results in various models are shown in Figure 2 in terms of the time derivative of aapp ≡ 1/(1 + z), the apparent cosmic scale factor that observers would deduce from the redshift assuming it arises only from cosmic expansion.

Figure 2: Time derivative of the apparent scale factor 1/(1 + z) in various cosmological models. The black curve shows the Planck cosmology, the flat ΛCDM fit to Planck observations of the CMB anisotropies. The BAO anomalies are in about 3σ tension with this model, motivating the grey curve showing a model where dark energy has an equation of state that varies linearly with a (Mirpoorian et al. 2025). Uncertainties on the present expansion rate are indicated in both cases. The coloured curves show results in local void models for three initial density profiles, adopting the best-fitting parameters in each case (Haslbauer et al. 2020). Note these parameter choices were not informed by BAO data. The pink shaded band shows the predicted present value in a model where the redshift of recombination is modified to try and best fit Planck and BAO data (Mirpoorian et al. 2025). The other shaded bands show the observed local cz’ according to two studies discussed further in the text. All shaded bands show predictions at the present epoch, so their extension to higher redshift is only for illustrative purposes. Note that the results here are most directly comparable to CC data. Predictions for other observables like the BAO angular scale and redshift depth cannot be trivially read off from this figure (Banik & Kalaitzidis 2025).

For now, BAOs provide the only major dataset that shows the Hubble tension emerge at low z despite being consistent with the Planck cosmology at high z. For this reason, I stressed the importance of getting additional BAO measurements at low z (Banik & Kalaitzidis 2025). For instance, the lowest z bin in the Dark Energy Spectroscopic Instrument (DESI) survey could be split into two bins, providing an additional measurement in a regime where any late-time or local solution to the Hubble tension would have a larger impact. The BAO anomalies are much smaller in percentage terms than the Hubble tension, but this should change as BAO measurements become available at lower z.

In terms of extending measurements outwards using techniques known to work at low z, the main issue at the moment is that SNe Ia provide the only way to test a possible return to the Planck cosmology with increasing z. The results so far indicate there is no such return, but none of the delegates believed this. It would be invaluable to extend other techniques like the TFR and FP out to z > 0.3, which would presumably show a return to the Planck cosmology if constraints from absolute and differential ages are to be trusted.

In general, the crucial issue going forward is to cover the relatively poorly explored z = 0.15 — 0.5 regime, either by extending techniques that work closer in out to higher z, or by extending techniques that work further out down to lower z. It seems very likely that the solution to the statistically significant Hubble tension will leave a significant imprint in this range of redshifts. In this way, we may hope to pin down what is actually responsible for the Hubble tension, which is surely one of the biggest issues facing cosmology at the moment.

Epilogue by Pavel Kroupa

I was not at this interesting meeting which Indranil aptly covers above, and I am quite astonished how the local void is being largely ignored despite all the observational evidence for it. It naturally leads to the Hubble tension (i.e., given the void there is no actual tension) because the void is still evolving and developing and leads to the galaxies falling to its sides like an apple falls to Earth. More worrying now is that the Planck cosmology may be wrong entirely, because of the problems with the CMB covered in DMC103-105 in the past three contributions. If most or even all of the CMB results from forming elliptical galaxies as comes out from the calculations of their luminosities (Gjergo & Kroupa 2025) then this cosmological Planck solution has no physical basis and the global expansion of the Universe becomes an unknown since the 600Mpc large KBC void affects the local apparent expansion and there would be many other voids, some potentially being even larger and even deeper with us being possibly in an encompassing 5Gpc void (Haslbauer, Kroupa & Jerabkova 2023). This would of course only be possible in a radically different cosmology than the ΛCDM model describes, but if true, then the overall expansion of the real Universe becomes rather unknown at the moment, since all available analysis is performed from the point of view of the ΛCDM model being correct or nearly correct if additional free parameters are added in the dark energy problem for example. The global expansion rate might be constrained by the oldest observed stars, but then we might be only seeing a local part of the real Universe in which star formation began delayed if it is underdense.

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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105. The contribution to the Cosmic Microwave Background radiation by the formation of galaxies at high-redshift

/ Prof. Dr. Pavel Kroupa / 5 Comments

The brightest and most massive galaxies today are ellipticals, and the stars born in them have synthesised within a billion years more heavy elements than the stars in our Galaxy over the long time span of 12 billion years.  The nuclear reactions needed to synthesise all of these elements made the elliptical galaxies brilliant “fire storms” in the early Universe near a redshift of about 18. The combined luminosity of all these galaxies provided a photon flux that amounts to at least 1.4 per cent of the measured cosmic microwave background (CMB) flux but more likely corresponds to that of the whole observed CMB. In view of the fluctuations in the CMB that are currently thought to be merely a thousandth of a percent of the CMB flux upon which is based the primordial power-spectrum that constitutes the initial condition for cosmological structure formation theory, this is a shocking but robust result with upheaving implications for all of cosmological theory. 

Based on the research paper “The impact of early massive galaxy formation on the cosmic microwave background“,  published in Nuclear Physics B, 2025

by Eda Gjergo and Pavel Kroupa.

Preamble by Pavel Kroupa

Having been granted an Isaac Newton Scholarship at Trinity College, I left sunny Perth in Australia in the autumn of 1988, arriving in very misty, moist and grey but famous Cambridge, a place of learning with centuries of most impressive achievements.  I was of course awe-struck by being in that place, but also truly heart-broken from what I had left behind in Perth. But at The Camelot of Astronomy, Martin Rees provided me with an overwhelmingly warm personal welcome, a deeply pleasant event forever cherished in my memory. One morning at IoA coffee, Martin Rees asked me a question along the following lines: “How much radiation did a forming elliptical galaxy produce?” I had no answer and I think he was referring to the amount of gravitational binding energy released as the matter, originally spread over a large volume, collapsed to the galaxy. Today I can say that thanks to many very talented and bright researchers I met on the path from there to the present, and notably now thanks to brilliant Eda Gjergo, we can answer this question. Unknowingly at that time, my steps towards the answer involved finding the key to the matter cycle in the Universe: understanding the shape and systematic variation of the distribution of the masses of stars when they are born is the key that unlocks the door to an unfathomable treasure chamber. This treasure chamber points to the process of how matter appears and cycles through the Universe. So the first step started with me just “simply” counting the stars surrounding our Sun with lessons from Gerard Gilmore and Christopher Tout. Later it involved understanding that all stars from in compact embedded star clusters in the dense clumps of molecular clouds and thus learning how star clusters evolve with lessons from Sverre Aarseth. I learned how important the chemical enrichment of galaxies and galactic chemo-dynamics is for understanding galaxy formation and evolution with lessons from Gerhard Hensler, by this time in Kiel in northern Germany, where the “quest for the holy grail” — I did not know I was searching for —  had taken me by then. It is only now though, through the collaboration with Eda Gjergo, a Chicago-educated cosmologist, dust expert and chemical-evolution sage,  who took the final steps with me at unlocking that door: Now, finally, we do know the answer to how bright elliptical galaxies were upon forming (and much more): their spectacular brightness comes from them needing to burn Hydrogen and Helium into higher elements at a breathtaking pace. These profuse nuclear processes in the cores of very huge numbers of massive stars were necessary to explain the present-day properties of these galaxies. And when the quantum physical processes were releasing photons from the nuclear processes, these star-forging brilliantly shining assembling galaxies were packed next to each other (about six per Planck-satellite pixel!) in the expanding young Cosmos. Their combined luminosity was so intense, that today we still see it – as part, and perhaps even all, of the Cosmic Microwave Background. I am keenly aware of the implications of this statement – with Eda we are in the above mentioned treasure chamber reading and understanding the secrets held within. Answering Martin Rees’ question thus brings us closer to finding the holy grail which seems to have finally crystallised out on the sky through unlocking the key to the unfathomable treasure chamber – a subject for future DMC contributions: how does the real Universe truly function? 

 There are two categories of galaxies

There are two broad categories of galaxies: the spiral galaxies which are razor thin disk galaxies in which gas clouds continuously form stars and the matter orbits around the galaxy’s centre on nearly circular orbits. Major disk galaxies consist of a few 1010 Msun (i.e. a few hundred billion Solar masses, one Msun being one Solar mass) in stars and a few 109 Msun in gas, both of which orbit around the centre at a near constant 200 km/s with diameters of some 40kpc (1 pc is 3.26 light years) and disk thickness of about 0.4 kpc. Our Milky Way is such a galaxy.  Sub categories of these are barred galaxies in which the matter in the inner parts, where the rotation curve is rising with distance until it reaches its constant value, orbits radially rather than circularly, and also lenticular galaxies which are puffed up and gas-depleted disk galaxies composed of older stars. Dwarf star forming galaxies contain more gas than stars and are merely little disk galaxies, for example the one-Mpc distant DDO210, a 1kpc sized dwarf  which has a mass of a massive globular star cluster, a few 106 Msun, but is forming molecular clouds (or “cloudlets”?) and stars (e.g. Lee et al. 1999, there appear to be no further more recent studies of this particularly interesting little galaxy).  Counting all the galaxies in some representative volume it turns out that about 97 per cent of all galaxies are such rotating disk galaxies. Lenticular galaxies only make about 10 per cent of the disk galaxy sample and so about 80-85 per cent of all galaxies are rotating thin disks that are continuously accreting gas that sustains approximately a constant level of star formation in each galaxy since it was born (Kroupa et al. 2020, Haslbauer et al. 2023,  Haslbauer et al. 2024).

The other major category of galaxies are  the rare elliptical galaxies, an example of which is shown in Fig.1. These also come in masses ranging from, 105 Msun or less up to a few times 1012 Msun (e.g. M87), the most massive ones thus being also the most massive known galaxies. The least massive “dwarf spheroidal galaxy” does not weigh more than a low-mass star cluster and is in most cases a satellite “galaxy” of a major galaxy. But (dwarf) elliptical galaxies less massive than 1010 Msun are distinctly different from the more massive ones as the dwarfs have a spatial stellar distribution within them very similar to disk galaxies without gas (exponential profile, puffed up rotating disk) while the more massive “classical” elliptical galaxies are roundish systems with a de Vaucouleurs’s density profile and are nearly without rotation.  These comprise only about 3-4 per cent of all galaxies more massive than about 1010 Msun and are mostly found in clusters of galaxies.  A review of the distribution of galaxies and their relative numbers has been provided by Binggeli et al. (1988). The fraction of  these classical elliptical galaxies did not change since the past 6 Gyr as observations tell us (Delgado-Serrano, Hammer et al. 2010).

Fig.1. The huge elliptical galaxy ESO 325-G004 – shone 10,000 times brighter when it formed than it does today. These types of galaxies briefly lit up the entire universe – and contributed to the background radiation we can measure today. © Image: NASA, ESA and The Hubble Heritage Team (STScI/AURA); J. Blakeslee (Washington State University)

The formation of elliptical galaxies

Elliptical galaxies today are “dead”, they have not been forming many stars since more than 10 Gyr ago (e.g. Salvador-Russinol et al. 2020), and they formed very rapidly when the Universe was young and so they are the oldest galaxies we know of.  We know this from many observations of many elliptical galaxies which analysed the composition of the light emitted by the thousands of billions of stars that are still alive (i.e. burning hydrogen into helium and beyond) in them. Spectroscopy and the analysis of their light tells us that the stars are ancient and the mixture of their elemental abundances tells us most of them formed in-bulk together very rapidly, within a Gyr or even less (e.g. Thomas et al 2010; McDermid et al. 2015;  Yan et al. 2021). 

We know a lot about the massive elliptical galaxies because we can basically touch them with our modern telescopes. 

How do we know that elliptical galaxies formed very fast?  Spectroscopic analysis tells us that the stars in them are iron rich, but also alpha-element rich. Alpha elements are elements in the periodic table that are created in fusion processes in massive stars through the addition of alpha particles (He nuclei). Massive stars (typically heavier than about 13 Suns) explode as core-collapse supernovae after a few Myr, thereby blowing off most of their matter. But the core of the star implodes to a neutron star or a stellar-mass black hole, taking most of the iron that the star had synthesised with it. Thus these stars release much of the alpha elements they synthesised but little iron. After about a Gyr the supernova type 1a begin to explode in a galaxy. These are white dwarfs that explode because they accrete mass from another star or merge with another white dwarf. These explosions also burn all elements and release all of them into space because the explosion destroys the star. Thus, when supernovae type 1a start to explode, the interstellar gas, enriched until now with alpha elements, begins to be also enriched by iron. The ratio  between the number of alpha elements and iron nuclei in a star thus tells us when the star formed relative to the start of star formation. So we “simply” need to take a spectrum of the stars in elliptical galaxies and measure this ratio as well as the amount of iron in the stars and thus in the galaxy. Because most of the stars in elliptical galaxies have a high alpha-element abundance relative to the iron abundance, we know that most of the stars had to be born from gas in the forming elliptical galaxy before the supernova type 1a started to explode, i.e., before about 1Gyr. 

But most cosmologists were convinced that elliptical galaxies formed at late cosmological times due to dry mergers, that is, from galaxies that already had no gas (in this sense our Milky Way Galaxy is “wet”). This would need to be the case in the hierarchical merger-driven build-up of galaxies in the standard ΛCDM model of cosmology since new stars are not allowed to be born during the mergers. Quite obviously,  such pre-merger “dry” galaxy building blocks are postulated and have never been observed to exist with the properties of their stars that would make them candidates for building blocks of observed elliptical galaxies (namely much alpha elements compared to iron, but also a lot of iron). Even today some still think this is the case and studies based on their structural properties are claimed to prove consistency with the observed galaxies (e.g. Ferreira et al. 2025). But the ages of the stellar particles in these model galaxies that from in the modern cosmological super-computer simulations are completely inconsistent with the ages of the stars in the real elliptical galaxies (Eappen et al. 2022): the merger-driven models in the ΛCDM cosmology yield elliptical-like galaxies with stellar particles in them that typically have age differences of about 5 Gyr, while the real elliptical galaxies have stars in them that span age differences that are <1Gyr. Also, the relative number of real elliptical galaxies is not increasing with time as mentioned above, while it does so in the ΛCDM cosmology because mergers continue to produce them. Indeed, the galaxy evolution community has now known for over two decades that massive elliptical galaxies (that are more luminous than a few times 1010 Solar luminosities) must have formed much quicker, and far sooner than spiral galaxies. Note that some of these early-formed elliptical galaxies that ended-up being in a more sparse environment appear to have been able to grow a disk around themselves. In such a case this ancient elliptical appears today as a classical bulge, as is the case in our Milky Way for example. 

A typical massive elliptical galaxy thus formed in a gigantic star formation “hyper-burst”  from the collapse of a primordial galaxy-scale gas cloud shortly after the Big Bang. In the collapse of such protogalactic clouds, thousands of solar masses of stars formed per year. In comparison, only approximately two solar masses of stars have been forming per year in our entire Milky Way, which is why it today has a mass in stars of about 5×1010 Msun. 

This rapid formation of a massive elliptical galaxy is easily understood in a cosmological model in which the Universe expands and is initially composed of gas only. Milgromian gravitation allows proto-galactic gas clouds to collapse and if these have the same initial physical radii of about 500kpc then the collapse occurs faster for the more massive ones as shown in Fig.2 reproducing in fact the observationally deduced formation times. 

Fig.2. The star formation histories of collapsing proto-galactic gas clouds with masses  (from top to bottom) of 10×1012, 7.0×1010, 6.4×1010, 5.4×1010, 3.0×1010, 1.0×1010 Msun all starting with a radius of 500 kpc. The black line is the time when the first star is formed in the models. Each model has been shifted in time according to the Thomas et al. (2005) age dating (their equations 11 and 12). The nearly transparent SFHs are relative to the start of the computation at t = 0. Note the naturally occurring downsizing phenomenon according to which more massive galaxies form more rapidly. Adapted from fig.6 in Eappen et al. (2022).

A challenge is to embed these results into a consistent cosmological model in which gravitation is Milgromian. We are working on this and it seems possible and we will document this Bohemian Model of Cosmology in an upcoming publication.

The rapid metal enrichment and the stars that are needed to do so

Returning to the formation of massive elliptical galaxies, we know that a very large number of massive stars needs to have formed in them over the formation time of a massive elliptical galaxy (a few hundred My), with each star being at least 10 to 20 times heavier than our Sun and living a few to a few dozen Myr. We know this because these galaxies contain many heavy elements (these are chemical elements heavier than Helium [for example Carbon, Oxygen, Silicon, Iron] and are referred to by astronomers as “metals”). A massive elliptical galaxy today consists of about a billion solar masses of metals. The synthesis of such a quantity of metals from hydrogen in the cores of massive stars through nuclear burning produces a tremendous amount of energy, which is what made elliptical galaxies so bright during their formation. Such massive stars shine a hundred thousand to a million times brighter than our Sun, but they die quickly, after a few million years after being born thereby releasing, through their supernova explosions, much of the metals that were created within them into the gas in the galaxy from which new stars form. After a few hundred million years the gas is either used up or heated too much for further star formation, all of the massive stars fade away and the young elliptical galaxy slowly evolves over a period of 12 billion years into the elliptical galaxies we see today.

The initial mass function of stars — the IMF

How did we describe the stellar populations that form in the elliptical galaxies?  Extracting the initial mass function of stars (the IMF), i.e., how many stars of a given mass are born together in a molecular cloud clump, is one of the most fundamental problems in astrophysics and cosmology. The best results are typically obtained if one research group systematically and continuously continues developing a problem, which is what I outline in the following: Progress started off by first understanding the distribution of stars in the neighbourhood of the Sun taking into account the intricacies of the stellar mass-luminosity relation for low-mass srtars (Kroupa, Tout & Gilmore 1990), unresolved binary stars (Kroupa, Tout & Gilmore 1991) and Galactic disk structure and its star formation history (Kroupa, Tout & Gilmore 1993), extending this to star counts in star-forming regions in the Milky Way and the Magellanic Clouds combined with deeply understanding how very young star clusters evolve and loose the stars born in them via an essential excursion into the Nbody dynamics research world (Kroupa 2001). A detailed look at populations of stars of different metallicities already informed of a possible metallicity dependence of the IMF for low-mass stars (Kroupa 2002). This long-term research programme that then also took into account the stellar populations and dynamical properties of ancient ultra compact dwarf galaxies (Dabringhausen, Kroupa & Baumgardt 2009, Dabringhausen, Fellhauer & Kroupa 2010, Dabringhausen et al. 2012) and globular star clusters (Marks et al. 2012) finally lead to the understanding how the mass distribution of freshly formed stars depends on the metallicity and density of the molecular cloud clump in which the embedded star cluster forms. By integrating all these embedded clusters over a whole galaxy (Kroupa & Weidner 2003) it became possible to calculate the galaxy-wide initial mass function of stars, and how it depends on the star-formation rate if the stellar IMF is invariant in shape (Weidner & Kroupa 2005), and on the metallicity and star-formation rate of the galaxy if the shape of the stellar IMF depends on metallicity and molecular cloud clump density as deduced from the above research programme by Marks et al. (2012, see Jerabkova et al. 2018 for a seminal paper on this). 

Through the thorough testing for self-consistency and agreement with local and extragalactic data, we now have much confidence as to how the stellar IMF varies on a molecular cloud clump scale and how the galaxy-wide IMF varies for different galaxies (Kroupa, Gjergo, Jerabkova & Yan 2024). 

This “IGIMF Theory” (integrated-galaxy-wide stellar IMF theory and the understanding of how the stellar IMF varies) was developed largely in Bonn  — many a thought being spent on this problem while walking in the Messdorfer Feld to and from the Institute — and allows us to calculate the stellar populations in the forming and evolving elliptical galaxies (Haslbauer et al. 2024; Zonoozi, Haghi & Kroupa 2025). In fact, it is the only known way to do this which also leads to the rapid enrichment with elements as is observed in the elliptical galaxies (Yan, Jerabkova & Kroupa 2021). While the IGIMF Theory is the only such theory around that self-consistently allows such calculations, the results concerning the CMB we are discussing here are not crucially dependent on the IGIMF Theory.  

The CMB-relevant results discussed here are a necessary outcome of the high metallicity of the elliptical galaxies and their rapid formation, requiring a very large number of massive stars for the synthesis of the elements and this is what makes the elliptical galaxies so bright. 

The brightness of a young elliptical galaxy

The nuclear reactions of the hundreds of billions (1011 – 1012) of massive stars generated a luminosity that was ten thousand times higher than the luminosity of today’s old elliptical galaxies. This is shown by the new calculations performed by us (Fig.3 and Fig.4 for all elliptical galaxies combined).  These calculations are documented in the publication “The Impact of Early Massive Galaxy Formation on the Cosmic Microwave Background.” This research was published in May of 2025 in the journal “Nuclear Physics B.”

Fig.3.  The evolution of the total (bolometric) luminosity of single massive elliptical galaxies (“ETGs”) of masses in all stars ever formed of 1013 and 1014 Msun, with time. The green dashed line is a self-consistent computation confirming the extreme peak brightness of such elliptical galaxies. These extreme brightnesses are a consequence of the nuclear reactions taking part in the massive stars that occurred in all massive elliptical galaxies in order to synthesise through nuclear fusion the large amount of observed metals in them. This is fig.2 in Gjergo & Kroupa (2025), see there for more details.

Fig.4. The total luminosity of all massive elliptical galaxies in the observable Universe combined assuming they formed in the redshift range 15 to 20. There would be about 44 million such galaxies with present-day masses of 1012 Msun distributed across the entire sky. This is fig.4 in Gjergo & Kroupa (2025), see there for more details.

The above has two important implications: On the one had side,  elliptical galaxies today mostly consist of dead stars (black holes, neutron stars, and white dwarfs), and the stars we see are merely a “sugar coating”.  The mass in neutron stars and black holes is five or more times larger than the mass in stars.

The stars in a present-day elliptical galaxy are merely the ambers in the ashes of a once-fierce firestorm.

Dust

The other implication is that the intense star-formation activity rapidly, within a few Myr, produced an immense amount of dust (e.g. Inoue 2011). Alone the mergers of many massive stars born in tight binaries in the dense hypermassive star-burst clusters forming in the innermost region of the forming elliptical galaxies would have expelled nuclear-processed material before supernovae contributed. This is directly related to the emergence of super-massive black holes there (Kroupa et al. 2020) as well as the phenomenon of “multiple stellar populations” in ancient hyper-massive star burst clusters that we see today as the massive old globular clusters (Wang et al. 2020). We know that dust enshrouds the star-formation activity from the dark clouds in our own Milky Way and also observed star bursting galaxies in the nearby Universe in which the star formation is deeply hidden in massive dust-laden molecular clouds, such as Arp 220, see e.g. Dabringhausen et al. (2012). Galaxies in fact radiate most of their energy near 100 micro m (0.1mm) as seen in Fig.5 which is fig.2 in Iyer et al. (2025).

Fig.5. The spectral energy distribution of a typical star-forming galaxy. Note the peak near 100 micro m which is star light absorbed and reemitted in the infrared emission by dust. This is fig.2 in Iyer et al. (2025), see there for more details.

When did the elliptical galaxies form?

Spectroscopic observations of elliptical galaxies inform us that the vast fraction of their stars formed very early in the Universe. These are very ancient galaxies. The more massive once formed not only faster but also earlier (Thomas et al. 2005). Very recent high-resolution observations even tell us when and how quickly, with the results obtained by (Jegatheesan et al. 2024) indicating elliptical galaxies to have started growing more than 14Gyr ago (i.e. nominally before the ΛCDM model universe existed).

In our calculations we applied the following reasoning: the Eappen et al. collapse results (Fig.2 above) imply, by matching the Thomas et al. (2005) formation time-scales to the simulated ones, that the elliptical galaxies formed from physical volumes with radii of about 400kpc. That is, they could not be separated by less than 800kpc. Today they have a separation of about 15Mpc. They would have thus been born at the earliest at a redshift of z=15/0.8 = 18.75. This coincides with the anomalous 21cm absorption line detected near a redshift of about 17 (e.g. McGaugh 2018) that may be mapping the overdensities of hydrogen gas which would have been driving the collapse of the gas clouds in which the elliptical galaxies formed. This redshift range of elliptical galaxy formation of about 15 to 20 matches well the observation by the James Webb Space Telescope (JWST) of massive galaxy formation detected at z>13 (e.g. Haslbauer et al. 2022).

With the separation of the forming elliptical galaxies we can calculate the luminosity density they were providing as they formed and evolved. The photons generated though the nuclear burning in their stars are still around — they have not left the Universe — just like the primordial CMB photons are still around that astronomers and physicist today think are from recombination at z=1100. The observed photon background is thus a sum of these ancient CMB photons and of the elliptical galaxies.

The contribution to the CMB by massive young elliptical galaxies

If galaxies emit, in their rest-frame, mostly near 0.1mm, then at a redshift of about 18 this corresponds to a wavelength of 1.9mm. This is the peak of the CMB emission as detected today. Our calculation assumes the star light in the forming elliptical galaxies to be thermalised by the dust formed in the starbursts, as observed for the nearby starbursts. The energy density of the infrared photons so created at redshifts 15-20 comes out to be today about equal to the energy density of CMB photons, but it contributes at least 1.4 per cent to it. This is shown in Fig.6 which is fig.5 in our paper (Gjergo & Kroupa 2025).

Fig.6. The energy density of infrared photons as a function of redshift. The red line shows the decrease (with decreasing redshift) of the CMB energy density as the Universe expands, the CMB photons being released from the cooling post-Hot-Big-Bang plasma at redshift z=1100 (the red cross). In the redshift range 15-20 (vertical grey region) massive elliptical galaxies form and they contribute a density in infrared photons shown as the other lines and the grey region towards decreasing z, depending on the assumptions made (e.g. on the average separation of elliptical galaxies in the Universe). Our most conservative estimate based on assuming the average separation between massive elliptical galaxies today is about 15 Mpc is the lowest curve. This is a conservative estimate based on the local density of elliptical galaxies because we are in a major matter underdensity spanning about 300Mpc in all directions, the KBC void (Haslbauer et al. 2020). This means that 1.4 per cent of the present-day CMB photon density comes from these galaxies. The more realistic estimate though suggests it is more, with massive elliptical galaxies possibly accounting for all CMB photons. This is fig.5 in Gjergo & Kroupa (2025), see there for more details.

Therefore, at least 1.4 per cent of the CMB peak flux comes from forming elliptical galaxies as they were building higher elements through the quantum-physical processes in the cores of their massive stars. But probably all of the CMB flux actually comes from these processes, this being the more natural result of the calculation. Subtracting this contribution from the observed CMB flux leaves between 86 per cent and zero per cent in the CMB produced through recombination at a redshift of 1100.

This alone already upsets Hot Big Bang cosmology as practiced today. But since the elliptical galaxies are not distributed uniformly on the sky this means that the power-spectrum today used to seed the initial conditions for structure formation in cosmological models has no physical meaning, because it describes the fluctuations in the CMB that are supposedly at a level of 1 in 105, i.e. one thousandth of a per cent — a fluctuating 1.4 per cent contribution clearly overrides this by many orders of magnitude. A schematic of the primordial CMB plus the contribution by elliptical galaxies is shown in Fig.7.

Fig.7. On the left is the “afterglow of the Hot Big Bang”, the recombination at a redshift of 1100 which released the photons from the hot gas which we (think we) see today as the redshifted CMB (the waves become red to the right). In the redshift range of 15 to 20 elliptical galaxies formed (the red circles) and also released infrared photons that today add to the observed CMB. The glowing ashes that once were the brilliantly bright elliptical galaxies are today seen as the small red dots in an otherwise expanding black Universe on the right. Copyright: Eda Gjergo.

An interesting and largely overlooked independent evidence that elliptical galaxies may indeed be related to the observed CMB is that the latter has more power in it and a higher temperature in the southern hemisphere where there is also a highly significant overpopulation of early-type galaxies (Fig.8 from Javanmardi & Kroupa 2017; for more details see point “pt2” on p.19 in the Corfu “tensions in cosmology” contribution from 2025).

Fig.8. This is from fig.6 in Javanmardi & Kroupa (2017) and shows the distribution on the sky of all galaxies with line of sight velocities relative to the CMB background less than 14000 km/s. Their morphological types are indicated by colour as defined in the key with red colours being early types (ellipticals) and blue being late-type star forming galaxies. The southern hemisphere has significantly more early-type galaxies. Behnam Javanmardi and me originally thought that this crazy result must be from some unknown bias in the reporting of the galaxy-types.

Implication:

We have thus seen above that there is even evidence that early-type galaxies seem to be linked to the CMB: they are significantly more abundant on the one hemisphere where the CMB is also warmer with more power in it. This strengthens the conclusions from our publication (Gjergo & Kroupa 2025) that elliptical galaxies indeed appear to be linked to the CMB.

The implication of this would be that the CMB’s role as evidence for a Hot Big Bang becomes unclear — in more drastic words by Pavel Kroupa: “The currently used CMB and the currently used initial power spectrum have no physical meaning in terms of an inflationary Hot Big Bang cosmology.”

In Conclusion:

We simply accept the observed properties of massive elliptical galaxies. Namely, they formed rapidly and before supernova type 1a explosions contributed a significant amount of Iron, between a redshift of 15 and 20, thereby synthesising, in this brief time, the large amount of metals we see in them. We find, given their present day separations, that they contributed a present-day flux of about 1.9mm photons that amounts to at least 1.4 per cent, and probably makes up all, of the observed about 1.9mm photons from the CMB. If correct, then this implies that everything being done in current cosmology in terms of structure formation based on the CMB power spectrum has no physical meaning and that cosmology will have to be rewritten taking into account the important role of forming elliptical galaxies.

Clearly, research must now (i) investigate what the true redshift z=1100 CMB looks like after subtracting this important foreground, (ii) explore which affect this has on Hot Big Bang based cosmological models and (iii) do calculations, modelling and theoretical development to understand the properties of this foreground (how black-body-like is it?). We need calculations (iv) of the evolution of the young ellipticals and (v) of their time-dependent dust content (the rapid formation and destruction of it). And, last not least, (vi) we need to research if and how a cosmological model can be developed that encompasses the very early formation of galaxies clearly documented also by the JWST.

Media:

YouTube video in English

Press release in English

Press release in Czech

Press release in German

Newsweek by Rachael O’Connor

Science News Today by Muhammad Tubin

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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104. Artificial Intelligence on the CMB and its Power Spectrum: Effects of Model Dependence

/ Prof. Dr. Pavel Kroupa / 1 Comment

On May 25th, 2025, AI Gemini 2.5 Pro (Google) was asked this question:
“How much does the observed CMB power spectrum depend on foreground cleaning and corrections for LCDM structure formation?“

Gemini’s answer:

This is a crucial question that gets at the practical realities and model-dependencies in CMB analysis. The observed CMB power spectrum is indeed significantly affected by both foreground cleaning and the effects of structure formation.

  1. Dependence on Foreground Cleaning:
    • Magnitude of Foregrounds: Foregrounds are emissions from astrophysical sources between us and the CMB’s last scattering surface. These include:
      • Our Galaxy (Milky Way): Synchrotron radiation (from electrons spiraling in magnetic fields), free-free emission (bremsstrahlung from ionized gas), and thermal dust emission. These are very bright, especially near the galactic plane.
      • Extragalactic Sources: Radio point sources (active galactic nuclei, star-forming galaxies) and the cumulative emission from distant dusty star-forming galaxies (the Cosmic Infrared Background, CIB, which bleeds into microwave frequencies).
      • Sunyaev-Zel’dovich (SZ) Effect: CMB photons scattering off hot electrons in galaxy clusters. This is both a foreground and a cosmological probe.
    • Necessity of Cleaning: These foregrounds can be orders of magnitude brighter than the tiny CMB anisotropies (1 part in 100,000). Without meticulous cleaning, the CMB power spectrum would be completely dominated and swamped by these foregrounds. It would be impossible to extract cosmological information.
    • Cleaning Techniques: Scientists use multi-frequency observations (e.g., Planck observed at 9 frequency bands). Since the CMB has a near-perfect blackbody spectrum, and foregrounds have different spectral signatures, these can be separated using sophisticated statistical techniques (“component separation”). This often involves:
      • Modeling the spectral and spatial characteristics of each foreground.
      • Fitting these models to the multi-frequency maps to subtract them.
      • Masking out the most contaminated regions (like the galactic plane or bright point sources).
    • Impact of Imperfect Cleaning: Foreground cleaning is never perfect. Residual foreground contamination is one of the largest sources of systematic uncertainty in CMB analysis.
      • On large angular scales (low ℓ in the power spectrum), galactic foregrounds are particularly challenging and can affect parameters like the optical depth to reionization (τ) and the scalar spectral index (ns).
      • On small angular scales (high ℓ), extragalactic point sources and the SZ effect become more important.
      • Polarization: CMB polarization signals (E-modes and especially B-modes) are much fainter than temperature anisotropies, making them even more susceptible to polarized foregrounds (like galactic dust and synchrotron). The search for primordial B-modes (a sign of inflationary gravitational waves) is critically dependent on exquisite foreground removal.
    • Model Dependence of Cleaning (ΛCDM relation):
      • The physical models for the foregrounds themselves (e.g., dust emission properties, synchrotron spectral indices) are based on astrophysics, not directly on ΛCDM cosmology.
      • However, the statistical assumptions made during component separation or the priors used in modeling can introduce subtle biases if not handled carefully.
      • The need to clean to an incredibly high precision is driven by the desire to test ΛCDM and measure its parameters accurately. So, while the cleaning methods might aim to be model-agnostic regarding cosmology, the goal is often to isolate a signal that is then interpreted within ΛCDM.
  2. Dependence on Corrections/Modeling of ΛCDM Structure Formation (Secondary Anisotropies):
    The photons from the last scattering surface don’t travel to us unimpeded. They interact with the large-scale structures that form over cosmic time, as predicted by models like ΛCDM. These interactions create “secondary anisotropies” superimposed on the primordial CMB.
    • Gravitational Lensing: As CMB photons travel through the universe, their paths are bent by the gravitational potentials of intervening large-scale structures (halos of dark matter, galaxy clusters).
      • Effect: This smooths out the acoustic peaks in the power spectrum slightly and transfers power from larger to smaller angular scales. It also generates B-mode polarization from primordial E-modes.
      • Handling: Lensing is a significant effect. Modern CMB analyses either:
        • Model the lensed spectrum: The theoretical ΛCDM power spectrum includes the effect of lensing.
        • De-lens the data: Attempt to reconstruct the lensing potential from the CMB itself (or from external large-scale structure tracers) and “correct” the observed power spectrum to estimate the unlensed primordial spectrum. This de-lensing process relies on assumptions about the properties of the lensing potential, which are informed by ΛCDM.
      • The lensing signal itself (its power spectrum) is a powerful cosmological probe and provides strong evidence for dark matter and consistency with ΛCDM predictions for structure growth.
    • Integrated Sachs-Wolfe (ISW) Effect: Photons gain or lose energy when passing through time-evolving gravitational potentials.
      • Early ISW: Occurs around the time of matter-radiation equality (part of the primary anisotropy calculation).
      • Late ISW: Occurs at later times when dark energy begins to dominate and accelerates cosmic expansion, causing gravitational potentials to decay. This affects the largest angular scales in the CMB.
      • Handling: The ISW effect is a predicted component of the CMB power spectrum within ΛCDM. Its detection (through cross-correlation with large-scale structure tracers) is considered evidence for dark energy.
    • Sunyaev-Zel’dovich (SZ) Effect: As mentioned, this is both a foreground and an effect of structure.
      • Thermal SZ: Hot gas in clusters boosts the energy of CMB photons.
      • Kinetic SZ: Doppler shift due to the bulk motion of clusters.
      • Handling: For primordial CMB studies, the tSZ is typically modeled and removed as a foreground. However, the SZ power spectrum itself contains information about structure formation and cluster astrophysics.
    • Model Dependence (ΛCDM): The prediction and interpretation of these secondary anisotropies are highly dependent on the ΛCDM model. ΛCDM dictates how structures grow, how dark energy influences expansion, and thus the expected magnitude and characteristics of lensing and ISW effects. If ΛCDM were significantly different, the predictions for these secondary effects would also change.

In summary:

  • Foreground Cleaning: Absolutely essential. The raw sky signal is massively dominated by foregrounds. The process aims to be astrophysically driven but residual contamination is a major concern. The target precision is set by what’s needed to test cosmological models like ΛCDM.
  • Structure Formation Effects (Secondary Anisotropies): These are inherent features of the CMB signal as it reaches us, caused by the universe evolving according to a cosmological model (like ΛCDM).
    • Gravitational lensing significantly alters the power spectrum and is either modeled or “corrected” for (de-lensing).
    • The ISW effect is a predicted component, especially at large scales.
    • The interpretation and modeling of these effects are fundamentally tied to ΛCDM (or whatever cosmological model is being used).

Therefore, the “observed CMB power spectrum” that cosmologists use to derive parameters is a highly processed product. It depends critically on the success of foreground removal (which tries to be independent of cosmological assumptions but is never perfect) and on how one accounts for or models the secondary anisotropies generated by structure formation (which is inherently model-dependent). Deviations from ΛCDM could manifest as an inability to consistently model all these aspects simultaneously or as tensions between parameters derived from different parts of the data.

End of Gemini’s answer:

In The Dark Matter Crisis by Elena Asencio and Pavel Kroupa. A listing of contents of all contributions is available here.

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