Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust

TL;DR

This paper develops a relativistic perturbation scheme for inhomogeneities evolving on a general, averaged background in cosmology, specifically for irrotational dust, addressing limitations of standard FLRW-based approaches.

Contribution

It introduces a new perturbation approach that accounts for a general background derived from spatial averaging, moving beyond traditional FLRW assumptions.

Findings

Derivation of a scalar perturbation scheme on a general background

Highlights the importance of averaged inhomogeneous evolution

Addresses limitations of standard FLRW-based models

Abstract

In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that (ii) the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model `irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.