Perturbation theory for cosmologies with nonlinear structure

Abstract

The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys will observe is to use cosmological perturbation theory for linear structures on horizon-sized scales, and Newtonian gravity for non-linear structures on much smaller scales. We propose a two-parameter formalism that generalizes this approach, thereby allowing interactions between large and small scales to be studied in a self-consistent and well-defined way. This uses both post-Newtonian gravity and cosmological perturbation theory, and can be used to model realistic cosmological scenarios including matter, radiation and a cosmological constant. We find that the resulting field equations can be written as a hierarchical set of perturbation equations. At leading-order, these equations allow us to recover a standard set of Friedmann equations, as well as a Newton-Poisson equation for the inhomogeneous part of the Newtonian energy density in an expanding background. For the perturbations in the large-scale cosmology, however, we find that the field equations are sourced by both non-linear and mode-mixing terms, due to the existence of small-scale structures. These extra terms should be expected to give rise to new gravitational effects, through the mixing of gravitational modes on small and large scales -effects that are beyond the scope of standard linear cosmological perturbation theory. We expect our formalism to be useful for accurately modelling gravitational physics in universes that contain non-linear structures, and for investigating the effects of non-linear gravity in the era of ultra-large-scale surveys.

A relativistic interpretation of bias in Newtonian simulations

“…We only demand the smallness of the metric perturbations while other perturbations, especially the matter density, may become arbitrarily large. See [23] for a more thorough discussion about our used weak-field definition which is in agreement with the employed weak-field scheme of [34][35][36][37].…”

General relativistic cosmological N-body simulations. Part I. Time integration

“…Nevertheless, these limitations can be circumvented to some extent with the help of analytical tools that were developed in the last decade. There are now refined perturbative expansions of the Einstein equations around the Friedmann-Lemaître-Robertson-Walker solution (FLRW) that are able to capture the non-linear matter dynamics [31][32][33][34][35][36][37][38][39][40]. Along with mapping techniques or appropriate gauge choices, one can then use Newtonian N -body simulations to effectively solve the non-linear dynamics of the relativistic theory .…”

Multi-scale perturbation theory. Part I. Methodology and leading-order bispectrum corrections in the matter-dominated era

“…In this section we will give a brief introduction to the methods used to find second-order solutions for scalar quantities in relativistic CPT. This will proceed in Poisson gauge, as this is the one commonly used gauge that remains valid in 2PPT [16,17]. The reader is referred to Refs.…”