Perturbation Theory in Lemaitre-Tolman-Bondi Cosmology

TL;DR

This paper develops a gauge-invariant linear perturbation theory for Lemaitre-Tolman-Bondi cosmology, crucial for comparing these models with observations like the Sachs-Wolfe effect and matter power spectrum.

Contribution

It introduces a fully general, gauge-invariant perturbation framework for LTB cosmology, revealing interactions among scalar, vector, and tensor modes and constructing new variables for clearer mode separation.

Findings

Scalar, vector, and tensor perturbations interact in LTB models.

New gauge-invariant variables are constructed that reduce to standard modes in homogeneous limits.

The theory facilitates rigorous comparison of LTB models with cosmological observations.

Abstract

The Lemaitre-Tolman-Bondi solution has received much attention as a possible alternative to Dark Energy, as it is able to account for the apparent acceleration of the Universe without any exotic matter content. However, in order to make rigorous comparisons between these models and cosmological observations, such as the integrated Sachs-Wolfe effect, baryon acoustic oscillations and the observed matter power spectrum, it is absolutely necessary to have a proper understanding of the linear perturbation theory about them. Here we present this theory in a fully general, and gauge-invariant form. It is shown that scalar, vector and tensor perturbations interact, and that the natural gauge invariant variables in Lemaitre-Tolman-Bondi cosmology do not correspond straightforwardly to the usual Bardeen variables, in the limit of spatial homogeneity. We therefore construct new variables that reduce to pure scalar, vector and tensor modes in this limit.