Observational constraints on cosmological future singularities

We verify the existence of Generalized Sudden Future Singularities (GSFS) in quintessence models with scalar field potential of the form V (φ) ∼ |φ| n where 0 < n < 1 and in the presence of a perfect fluid, both numerically and analytically, using a proper generalized expansion ansatz for the scale factor and the scalar field close to the singularity. This generalized ansatz includes linear and quadratic terms, which dominate close to the singularity and cannot be ignored when estimating the Hubble parameter and the scalar field energy density; as a result, they are important for analysing the observational signatures of such singularities. We derive analytical expressions for the power (strength) of the singularity in terms of the power n of the scalar field potential. We then extend the analysis to the case of scalar tensor quintessence models with the same scalar field potential in the presence of a perfect fluid, and show that a Sudden Future Singularity (SFS) occurs in this case. We derive both analytically and numerically the strength of the singularity in terms of the power n of the scalar field potential.

We obtain the analogues of the Friedman equations in an emergent gravity scenario in the presence of dark energy. The background metric is taken to be Friedman-Lemaitre-Robertson-Walker (FLRW). We show that if $\dot\phi ^{2}$ is the dark energy density (in units of the critical density) then (a) for total energy density greater than the pressure (non-relativistic scenario, matter domination) the deceleration parameter $q(t)\approx\frac {1}{2} [1 + 27 \dot\phi ^{2}+...] &gt; \frac{1}{2}$ (b) for total energy density equal to 3 times the pressure (relativistic case, radiation domination), the deceleration parameter $q(t)\approx 1 + 18\dot\phi ^{2} +... &gt; 1$ and (c) for total energy density equal to the negative of the pressure (dark energy scenario), the deceleration parameter $q(t)&lt; -1$. Our results indicate that many aspects of standard cosmology can be accommodated with the presence of dark energy right from the beginning of the universe where the time parameter $t\equiv \fra...

Arxiv preprint arXiv:0903.4775, 2009

We consider perturbative modifications of the Friedmann equations in terms of energy density corresponding to modified theories of gravity proposed as an alternative route to comply with the observed accelerated expansion of the universe. Assuming that the present matter content of the universe is a pressureless fluid, the possible singularities that may arise as the final state of the universe are surveyed. It is shown that, at most, two coefficients of the perturbative expansion of the Friedman equations are relevant for the analysis. Some examples of application of the perturbative scheme are included.

Journal of Cosmology and Astroparticle Physics, 2014

We use the effective field theory of dark energy to explore the space of modified gravity models which are capable of driving the present cosmic acceleration. We identify five universal functions of cosmic time that are enough to describe a wide range of theories containing a single scalar degree of freedom in addition to the metric. The first function (the effective equation of state) uniquely controls the expansion history of the universe. The remaining four functions appear in the linear cosmological perturbation equations, but only three of them regulate the growth history of large scale structures. We propose a specific parameterization of such functions in terms of characteristic coefficients that serve as coordinates in the space of modified gravity theories and can be effectively constrained by the next generation of cosmological experiments. We address in full generality the problem of the soundness of the theory against ghost-like and gradient instabilities and show how the space of non-pathological models shrinks when a more negative equation of state parameter is considered. This analysis allows us to locate a large class of stable theories that violate the null energy condition (i.e. super-acceleration models) and to recover, as particular subsets, various models considered so far. Finally, under the assumption that the true underlying cosmological model is the Λ Cold Dark Matter (ΛCDM) scenario, and relying on the figure of merit of EUCLID-like observations, we demonstrate that the theoretical requirement of stability significantly narrows the empirical likelihood, increasing the discriminatory power of data. We also find that the vast majority of these non-pathological theories generating the same expansion history as the ΛCDM model predict a different, lower, growth rate of cosmic structures.

International Journal of Modern Physics D, 2009

Within the context of standard cosmology, an accelerating universe requires the presence of a third "dark" component of energy, beyond matter and radiation. The available data, however, are still deemed insufficient to distinguish between an evolving dark energy component and the simplest model of a time-independent cosmological constant. In this paper, we examine the cosmological expansion in terms of observer-dependent coordinates, in addition to the more conventional comoving coordinates. This procedure explicitly reveals the role played by the radius Rh of our cosmic horizon in the interrogation of the data. (In Rindler's notation, Rh coincides with the "event horizon" in the case of de Sitter, but changes in time for other cosmologies that also contain matter and/or radiation.) With this approach, we show that the interpretation of dark energy as a cosmological constant is clearly disfavored by the observations. Within the framework of standard Friedmann-Robertson-Walker cosmology, we derive an equation describing the evolution of Rh, and solve it using the WMAP and Type Ia supernova data. In particular, we consider the meaning of the observed equality (or near-equality) Rh(t0) ≅ ct0, where t0 is the age of the universe. This empirical result is far from trivial, for a cosmological constant would drive Rh(t) toward ct (t is the cosmic time) only once — and that would have to occur right now. Though we are not here espousing any particular alternative model of dark energy, for comparison we also consider scenarios in which dark energy is given by scaling solutions, which simultaneously eliminate several conundrums in the standard model, including the "coincidence" and "flatness" problems, and account very well for the fact that Rh(t0) ≈ ct0.

Physical Review D, 2006

We investigate the effects of viscosity terms depending on the Hubble parameter and its derivatives in the dark energy equation of state. Such terms are possible if dark energy is a fictitious fluid originating from corrections to the Einstein general relativity as is the case for some braneworld inspired models or fourth order gravity. We consider two classes of models whose singularities in the early and late time universe have been studied by testing the models against the dimensionless coordinate distance to Type Ia Supernovae and radio-galaxies also including priors on the shift and the acoustic peak parameters. It turns out that both models are able to explain the observed cosmic speed up without the need of phantom (w < −1) dark energy. 98.80.Es, 97.60.Bw, 98.70.Vc

The effective anisotropic stress  $\eta= −\Phi/\Psi is a key variable in the characterisation of the physical origin of the dark energy. It is however important to use a fully model-independent approach when measuring  to avoid introducing a theoretical bias into the results. We forecast the precision with which future large surveys can determine $\eta$  in a way that only relies on directly observable quantities, using the joint combination of Galaxy Clustering, Weak Lensing and Supernovae probes. Among the results, we find that a future large scale survey can constrain $\eta$  to within 10% if k-independent, and to within 60% if it is restricted to follow the Horndeski model. In order to find current constraints on  data for the growth rate $f\sigma_8$ coming from Redshift Space Distortion measurements, observations of the Hubble expansion $H(z)$, and a constraint for the quantity $P_2$ defined as the expectation value of the ratio between galaxy-galaxy and galaxy-velocity cross correlations, have been used. We find a value at $z = 0.32$ of  $\eta = 0.646 ± 0.678$, in agreement with the predicted value for the LCDM model. Finally, we produce a cosmological exclusion plot for modified gravity in analogy with the exclusion plots produced in laboratory experiments.

Physics Letters B, 2009

In this paper we study the final fate of the universe in modified theories of gravity. As compared with general relativistic formulations, in these scenarios the Friedmann equation has additional terms which are relevant for low density epochs. We analyze the sort of future singularities to be found under the usual assumption the expanding Universe is solely filled with a pressureless component. We report our results using two schemes: one concerned with the behavior of curvature scalars, and a more refined one linked to observers. Some examples with a very solid theoretical motivation and some others with a more phenomenological nature are used for illustration.

2014

Latin indices from the beginning of the alphabet, a, b, c, and so on generally run over four spacetime indices 0, 1, 2, 3, where v 0 denotes the time component of the vector v a. An exception to this convention occurs in paper V and the related section in chapter 5 where they label spatial coordinate indices from 1 to 3. Greek indices from the beginning of the alphabet, α, β, γ, and so on generally run over three spatial indices 1, 2, 3, and are used to label components relative an orthonormal frame, except in paper V where they label spacetime components from 1 to 4. Greek indices from the middle of the alphabet, μ, ν, and so on are used to label spacetime coordinate components. Latin indices from the middle of the alphabet, i, j, k, and so on are used to label spatial coordinate components, or as in paper IV, components relative a group invariant frame. Repeated upper and lower indices are summed over, unless otherwise indicated. The metric has signature − + + +. Units for which 8πG = 1 and c = 1, where G is the gravitational constant and c is the speed of light, are used throughout the thesis. Vectors and tensors are represented by symbols in bold font, x, 0, g, T for example, where the dimension and rank should be discernable from the context. 2 The cosmological constant was first introduced by Einstein [23] as a way to obtain a static universe, but was abandoned by him when it was discovered that the universe is expanding, only later to be revived in light of the new observations of an accelerating universe. 3 The names dark matter/energy are a bit misleading. It may sound like dark matter is completely black, absorbing all light, but in reality it is totally transparent, not interacting with light or normal matter at all, except through its gravitational pull (and possibly through weak interactions that are of no relevance on astronomical scales). More appropriate names would be invisible matter/energy. 4 Aleksander Aleksanderoviq Friedman's last name is sometimes translated Friedmann and sometimes Friedman.

Annalen Der Physik, 2010

One of the key challenges facing cosmologists today is the nature of the mysterious dark energy introduced in the standard model of cosmology to account for the current accelerating expansion of the universe. In this regard, many other non-standard cosmologies have been proposed which would eliminate the need to explicitly include any form of dark energy. One such model is the Sudden Future Singularity (SFS) model, in which no equation of state linking the energy density and the pressure in the universe is assumed to hold. In this model it is possible to have a blow up of the pressure occurring in the near future while the energy density would remain unaffected. The particular evolution of the scale factor of the Universe in this model that results in a singular behaviour of the pressure also admits acceleration in the current era as required. In this paper we compare an example SFS model with the current data from high redshift supernovae, baryon acoustic oscillations (BAO) and the cosmic microwave background (CMBR). We explore the limits placed on the SFS model parameters by these current data and discuss the viability of the SFS model in question as an alternative to the standard concordance cosmology.

Physics of the Dark Universe, 2017

We carry out an analysis of the cosmological perturbations in general relativity for three different models which are good candidates to describe the current acceleration of the Universe. These three setups are described classically by perfect fluids with a phantom nature and represent deviations from the most widely accepted ΛCDM model. In addition, each of the models under study induce different future singularities or abrupt events known as (i) Big Rip, (ii) Little Rip and (iii) Little Sibling of the Big Rip. Only the first one is regarded as a true singularity since it occurs at a finite cosmic time. For this reason, we refer to the others as abrupt events. With the aim to find possible footprints of this scenario in the Universe matter distribution, we not only obtain the evolution of the cosmological scalar perturbations but also calculate the matter power spectrum for each model. We have carried the perturbations in the absence of any anisotropic stress and within a phenomenological approach for the speed of sound. We constrain observationally these models using several measurements of the growth rate function, more precisely f σ8, and compare our results with the observational ones.

2020

We introduce a modified form of the Phenomenologically Emergent Dark Energy (PEDE) model by showing a very elegant approach. The model is named as Modified Emergent Dark Energy (MEDE) to distinguish from PEDE model and it includes $\Lambda$CDM, PEDE model, Chevallier-Polarski-Linder model and other cosmological models of interest. We show that the present article offers a very fantastic route to construct other PEDE models in a simple but very elegant way. The model has seven free parameters where the six parameters are the same as in $\Lambda$CDM or PEDE model and the remaining one parameter `$\alpha$&#39; quantifies the generalization. The present model predicts that dark energy equation of state at present assumes, $w_{\rm DE}\; (z=0) = -1 - \frac{\alpha}{3 \ln (10)}$ and in the far future (i.e., for $z \longrightarrow -1$), it will evolve asymptotically to $w_{\rm DE} \longrightarrow -1$. We perform a very robust observational analysis of the model using various observational da...

Journal of Physics: Conference Series, 2005

We review recent work and present new examples about the character of singularities in globally and regularly hyperbolic, isotropic universes. These include recent singular relativistic models, tachyonic and phantom universes as well as inflationary cosmologies.

Journal of Cosmology and Astroparticle Physics, 2010

We study F (R) modified gravity models which are capable of driving the accelerating epoch of the Universe at the present time whilst not destroying the standard Big Bang and inflationary cosmology. Recent studies have shown that a weak curvature singularity with |R| → ∞ can arise generically in viable F (R) models of present dark energy (DE) signaling an internal incompleteness of these models. In this work we study how this problem is cured by adding a quadratic correction with a sufficiently small coefficient to the F (R) function at large curvatures. At the same time, this correction eliminates two more serious problems of previously constructed viable F (R) DE models: unboundedness of the mass of a scalar particle (scalaron) arising in F (R) gravity and the scalaron overabundance problem. Such carefully constructed models can also yield both an early time inflationary epoch and a late time de Sitter phase with vastly different values of R. The reheating epoch in these combined models of primordial and present dark energy is completely different from that of the old R + R 2 /6M 2 inflationary model, mainly due to the fact that values of the effective gravitational constant at low and intermediate curvatures are different for positive and negative R. This changes the number of e-folds during the observable part of inflation that results in a different value of the primordial power spectrum index. 1. Introduction 1 2. Review of cosmological evolution 7 2.1 Non-linear oscillations and existence of a "sudden" singularity with |R| → ∞ 8 2.2 General viable F (R) models of present DE 11 2.3 Determination of the Hubble parameter 12 2.4 Structure of a singularity with F ′′ (R) = 0 for a finite R 13 3. Avoiding the weak singularity and solving the problems of F (R) DE models 13 4. Inflation and late time acceleration from one F (R) function 17 4.1 New problem 18 4.2 Resolution of the problem and the improved AB model 19 4.3 de Sitter attractors 19 4.4 Slow-roll inflation 20 4.5 Reheating 21 4.5.1 Evolution of H(t) without backreaction 22 4.5.2 Effect of backreaction 27 4.6 Cosmological evolution 29 5. Conclusions and discussion 32

Physics Essays, 2017

This article is a continuation of a former article, taking account of recent observational results a.o. from the Planck mission. The adopted approach starts considering a hot big bang scenario for an universe with Friedmann-Lemaître-Robertson-Walker (FLRW) metric, the spatial curvature parameter k = 0 and the cosmological constant Λ= 0. It does not contradict the standard model (now called « Λ-CDM model ») except on a point : the acceleration of the expansion of the universe is not related to the cosmological constant but to a « dark energy » component α which is mostly constant in time and is a constitutive part of the Hubble parameter. Using a reversed method, it is shown that the scale factor evolves in a similar way as in the Λ-CDM model for the past epochs but that the acceleration in the future is less pronounced. The evolution of several cosmological parameters from the end of an inflationary stage till now is given as was done in the former article. The major difference is that, instead of imposing the pressure to be nil at present time in order to comply with the equation of state for the matter-dominated era, the pressure – density ratio is left free to be negative. The pressure then naturally becomes negative around 7.12 Gyrs after the big bang. It is shown that the contribution of dark energy is negligible during the radiation-dominated era but becomes of the order of the contribution of matter during the matter-dominated era which solves the coincidence problem.