Related papers: A Relativistic view on large scale N-body simulati…
Cosmological perturbations with wavelengths smaller than Hubble radius can be handled in the context of Newtonian theory with very high accuracy. The application of this Newtonian approximation, however, is restricted to nonrelativistic…
The gravitational instability of inhomogeneities in the expanding universe is studied by the relativistic second-order approximation. Using the tetrad formalism we consider irrotational dust universes and get equations very similar to those…
Simulations of purely self-gravitating N-body systems are often used in astrophysics and cosmology to study the collisionless limit of such systems. Their results for macroscopic quantities should then converge well for sufficiently large…
The gravitationally-driven evolution of cold dark matter dominates the formation of structure in the Universe over a wide range of length scales. While the longest scales can be treated by perturbation theory, a fully quantitative…
We present a framework for general relativistic N-body simulations in the regime of weak gravitational fields. In this approach, Einstein's equations are expanded in terms of metric perturbations about a Friedmann-Lema\^itre background,…
Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore…
To explain the rich structure of voids, clusters, sheets, and filaments apparent in the Universe, we present evidence for the convergence of the two classic approaches to gravitational clustering, the ``pancake'' and ``hierarchical''…
We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the…
Large redshift surveys of galaxies and clusters are providing the first opportunities to search for distortions in the observed pattern of large-scale structure due to such effects as gravitational redshift. We focus on non-linear scales…
This work discusses the main analogies and differences between the deterministic approach underlying most cosmological N-body simulations and the probabilistic interpretation of the problem that is often considered in mathematics and…
The proper general relativistic description of the observed galaxy power spectrum is substantially different from the standard Newtonian description on large scales, providing a unique opportunity to test general relativity on horizon…
Within a cosmological context, we study the behaviour of collisionless particles in the weak field approximation to General Relativity, allowing for large gradients of the fields and relativistic velocities for the particles. We consider a…
A quantitative theory, based on the Zeldovich approximation, to provide an approximate description of the evolution of structure is presented. We give an expression for the characteristic scale of superlarge-scale structure which can also…
In this work we study the cosmological simulations as a tool to understand the formation of large-scale structure of the universe, for this, we show the equivalence of Newtonian cosmology with Poisson gauge and we study the solution of the…
We develop the effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium, apply it to a homogeneous universe with small density fluctuations. Keeping the density fluctuation up to the…
We present the second-order general relativistic description of the observed galaxy number density in a cosmological framework. The observed galaxy number density is affected by the volume and the source effects, both of which arise due to…
Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations. In an era of precision cosmology, we should ask: are these approximate…
Both for the background world model and its linear perturbations Newtonian cosmology coincides with the zero-pressure limits of relativistic cosmology. However, such successes in Newtonian cosmology are not purely based on Newton's gravity,…
This year marks the 100th anniversary of the birth of Yakov Zel'dovich. Amongst his many legacies is the Zel'dovich approximation for the growth of large-scale structure, which remains one of the most successful and insightful analytic…
We compare different nonlinear approximations to gravitational clustering in the weakly nonlinear regime, using as a comparative statistic the evolution of non-Gaussianity which can be characterised by a set of numbers $S_p$ describing…