The large scale structure formation in an expanding universe

An introduction to modern theories for the origin of structure in the Universe is given. After a brief review of the growth of cosmological perturbations in an expanding Universe and a summary of some important observational results, the lectures focus on the inflationary Universe scenario and on topological defect models of structure formation. A summary of the theory and current observational status of cosmic microwave background temperature fluctuations is given. The final chapter is devoted to some speculative ideas concerning the connection between cosmology and fundamental physics, in particular to ways in which the singularity problem of classical cosmology may be resolved.

2016

In the current paper, we have studied the effect of dark energy on formation where dark energy exists in the background. For this purpose, we used both WMAP9 and Planck data to study how the radius changes with redshift in these models. We used different data sets to fix the cosmological parameters to obtain a solution for a spherical region under collapse. The mechanism of structure formation for dark and baryonic matter is different. When processed by gravitational instability, density perturbations have given rise to collapsed dark matter structures, called halos. These dark matter halos offer the backdrop for the subsequent formation of all collapsed baryonic structures, including stars, galaxies, and galaxy clusters. In Planck Data forΛCDM , with the presence of dark energy in the background, the formation of baryonic matter is delayed. Therefore, it is a factor for the largening of the baryonic matter radius. Accompanying dark energy is entailing an increment of dark matter vi...

The European Physical Journal B, 2006

Models of structure formation in the universe postulate that matter distributions observed today in galaxy catalogs arise, through a complex non-linear dynamics, by gravitational evolution from a very uniform initial state. Dark matter plays the central role of providing the primordial density seeds which will govern the dynamics of structure formation. We critically examine the role of cosmological dark matter by considering three different and related issues: Basic statistical properties of theoretical initial density fields, several elements of the gravitational many-body dynamics and key correlation features of the observed galaxy distributions are discussed, stressing some useful analogies with known systems in modern statistical physics.

Physical Review D, 2004

We revise the statistical properties of the primordial cosmological density anisotropies that, at the time of matter radiation equality, seeded the gravitational development of large scale structures in the, otherwise, homogeneous and isotropic Friedmann-Robertson-Walker flat universe. Our analysis shows that random fluctuations of the density field at the same instant of equality and with comoving wavelength shorter than the causal horizon at that time can naturally account, when globally constrained to conserve the total mass (energy) of the system, for the observed scale invariance of the anisotropies over cosmologically large comoving volumes. Statistical systems with similar features are generically known as glass-like or lattice-like. Obviously, these conclusions conflict with the widely accepted understanding of the primordial structures reported in the literature, which requires an epoch of inflationary cosmology to precede the standard expansion of the universe.

Nature, 2006

The past two and a half decades have seen enormous advances in the study of cosmic structure, both in our knowledge of how it is manifest in the large-scale matter distribution, and in our understanding of its origin. A new generation of galaxy surveys -the 2-degree Field Galaxy Redshift Survey, or 2dFGRS 1 , and the Sloan Digital Sky Survey, or SDSS 2 -have quantified the distribution of galaxies in the local Universe with a level of detail and on length scales that were unthinkable just a few years ago. Surveys of quasar absorption and of gravitational lensing have produced qualitatively new data on the distributions of diffuse intergalactic gas and of dark matter. At the same time, observations of the cosmic microwave background radiation, by showing us the Universe when it was only about 400,000 years old, have vindicated bold theoretical ideas put forward in the 1980s regarding the contents of the Universe and the mechanism that initially generated structure shortly after the Big Bang. The critical link between the early, near-uniform Universe and the rich structure seen at more recent times has been provided by direct numerical simulation. This has made use of the unremitting increase in the power of modern computers to create ever more realistic virtual universes: simulations of the growth of cosmic structure that show how astrophysical processes have produced galaxies and larger structures from the primordial soup. Together, these advances have led to the emergence of a 'standard model of cosmology' which, although seemingly implausible, has nevertheless been singularly successful. strikingly illustrates how well this standard model can fit nearby structure. The observational wedge plots at the top and at the left show subregions of the SDSS and 2dFGRS, illustrating the large volume they cover in comparison to the ground-breaking Center for Astrophysics (CfA) galaxy redshift survey 3 carried out during the 1980s (the central small wedge). These slices through the local three-dimensional galaxy distribution reveal a tremendous richness of structure. Galaxies, groups and clusters are linked together in a pattern of sheets and filaments that is commonly known as the 'cosmic web' 4 . A handful of particularly prominent aggregations clearly stand out in these images, the largest containing of the order of 10,000 galaxies and extending for several hundred million light years. The corresponding wedge plots at the right and at the bottom show similarly constructed surveys of a virtual universe, the result of a simulation of the growth of structure and of the formation of galaxies in the current standard model of cosmology. The examples shown were chosen among a set of random 'mock surveys' to have large structures in similar positions to the real surveys. The similarity of structure between simulation and observation is striking, Research over the past 25 years has led to the view that the rich tapestry of present-day cosmic structure arose during the first instants of creation, where weak ripples were imposed on the otherwise uniform and rapidly expanding primordial soup. Over 14 billion years of evolution, these ripples have been amplified to enormous proportions by gravitational forces, producing ever-growing concentrations of dark matter in which ordinary gases cool, condense and fragment to make galaxies. This process can be faithfully mimicked in large computer simulations, and tested by observations that probe the history of the Universe starting from just 400,000 years after the Big Bang.

2013

The next generation of telescopes will usher in a new era of precision cosmology capable of determining key parameters of a cosmological model to percent level and beyond. For this to be effective, the theoretical model must be understood to at least the same level of precision. A range of subtle physical spacetime effects remain to be explored theoretically, for example, the effect of backreaction on cosmological observables. A good understanding of this effect is paramount given that it is a consequence of any space-time theory of gravity. We provide a comprehensive study of this effect from the perspective of geometric averaging on a hyper-surface and averaging on the celestial sphere. We concentrate on Friedmann-Lemaitre-Robertson-Walker spacetime with small perturbation up to non-linear order. This enables us to quantify by how much this effect could change the standard model interpretation of the universe. We study in great detail key parameters of the standard model, Hubble rate, deceleration parameter and area distance. We find that the Hubble rate depends on the choice of definition of the Hubble rate and the spatial surface on which the average is performed. Within the ΛCDM model, the backreaction effect on the background Hubble rate is of order 1% at a scale of 100 Mpc, and much less on larger scales. We find that for the deceleration parameter adapted to observation, the perturbation theory gives divergent answers in the UV and corrections to the background are of order unity or more depending on the choice of UV cutoff. For the area distance, we identify a range of new lensing effects, which include: double-integrated and nonlinear integrated Sach-Wolfe contributions, transverse Doppler effects in redshift space distortions, lensing from the induced vector mode and gravitational wave backgrounds, in addition to lensing from the secondorder potential and we also identify a new double-coupling between the density fluctuations integrated along the line of sight, and gradients in the density fluctuations coupled to transverse velocities along the line of sight. We conclude that the precision cosmology would be unsuccessful without the effect of backreaction being properly taking into account in parameter estimation. Also we need to rethink our theoretical approach to sub-horizon universe because un-renormalized perturbation theory appear not to be working. I would like to thank Camille Bonvin and Ruth Durrer for useful technical discussions on area distance in cosmology. I appreciate a detailed email clarifying the technical subtleties associated with switching of averaging hyper-surface by Giovanni Marozzi. I would also like to thank Gabriele Veneziano and his collaborators for comments on the first draft of the area distance paper. I would like to thank Alex Weigand and Dominik Schwarz for comments on the fitting formula for the averaged Hubble rate and the relationship with their work. I appreciate discussion with Albert Stebbins on constructing observable quantities. I also owe a special thanks to my office mate and friend Sean February for discussion and proofreading part of the thesis. I am grateful to Cyril Pitrou and JP Uzan for discussions on many aspects of this work and other unpublished works. I am very grateful to Sean Hartnoll for saving me from self-destruction during my Msc studies and after. I am highly indebted to Astrophysics section of department of Physics Oxford University for hospitality during the time I spent with them. I appreciate every special assistance given to me especially by Pedro Ferreira , Tim Clifton, Phil Bull, Sarah White, Krzysztof Bolejko, Edward Macaulay, and all the graduate students in the group. I would like to thank in a special way my supervisors: Chris Clarkson and George F. R. Ellis for both academic and personal guidance and assistance. I owe a special thanks to George for reading through every paragraph of this thesis. I am very grateful for this. Most of the computations here were done with the help of the tensor algebra package xPert/xAct [1] and xPand which I developed in collaboration with Cyril Pitrou and Xavier Roy.

arXiv (Cornell University), 2004

The evolution of matter density perturbations in two-component model of the Universe consisting of dark energy (DE) and dust-like matter (M) is considered. We have analyzed it for two kinds of DE with ω = −1: a) unperturbed energy density and b) perturbed one (uncoupled with matter). For these cases the linear equations for evolution of the gauge-invariant amplitudes of matter density perturbations are presented. It is shown that in the case of unperturbed energy density of DE the amplitude of matter density perturbations grow slightly faster than in the second case.

2013

Abstract. We propose a phenomenological generalization of the models of large–scale structure formation in the Universe by gravitational instability in two ways: we include pressure forces to model multi–streaming, and noise to model fluctuations due to neglected short–scale physical processes. We show that pressure gives rise to a viscous–like force of the same character as the one introduced in the adhesion model, while noise leads to a roughening of the density field, yielding a scaling behavior of its correlations. Key words: gravitation – hydrodynamics – instabilities – methods: analytical – cosmology: theory – cosmology: large-scale structure of Universe 1.

In the current paper, we have studied the effect of dark energy on formation where dark energy exists in the background. For this purpose, we used both WMAP9 and Planck data to study how the radius changes with redshift in these models. We used different data sets to fix the cosmological parameters to obtain a solution for a spherical region under collapse. The mechanism of structure formation for dark and baryonic matter is different. When processed by gravitational instability, density perturbations have given rise to collapsed dark matter structures, called halos. These dark matter halos offer the backdrop for the subsequent formation of all collapsed baryonic structures, including stars, galaxies, and galaxy clusters. In Planck Data forΛCDM , with the presence of dark energy in the background, the formation of baryonic matter is delayed. Therefore, it is a factor for the largening of the baryonic matter radius. Accompanying dark energy is entailing an increment of dark matter vi...

2006

We inquire the phenomena of clustering of galaxies in an expanding universe from a theoretical point of view on the basis of thermodynamics and correlation functions. The partial differential equation is developed both for the point mass and extended mass structures of a two-point correlation function by using thermodynamic equations in combination with the equation of state taking gravitational interaction between particles into consideration. The unique solution physically satisfies a set of boundary conditions for correlated systems and provides a new insight into the gravitational clustering problem.