Evolution of linear perturbations in Lema\^itre-Tolman-Bondi void models

TL;DR

This paper develops a numerical method to study how linear perturbations evolve in LTB void models, revealing significant coupling effects that impact cosmological observations like supernova distance measurements.

Contribution

It introduces a finite element numerical scheme for evolving coupled gauge-invariant perturbations in LTB models with realistic initial conditions.

Findings

Significant coupling up to 25% in large Gpc-scale voids.

Coupling effects influence the interpretation of supernova distance data.

Method enables detailed statistical analysis of perturbation evolution in inhomogeneous cosmologies.

Abstract

We study the evolution of linear perturbations in a Lema\^itre-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations to couple at first order. As shown by Clarkson et al. (2009), the evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We present a new numerical scheme using finite element methods to solve this equation system and generate scalar initial conditions based on Gaussian random fields with an underlying power spectrum for the Bardeen potential. After spherical harmonic decomposition, the initial fluctuations are propagated in time and estimates of angular power spectra of each gauge invariant variable are computed as functions of redshift. This allows to analyse the coupling strength in a statistical way. We find significant couplings up to $25\%$ for large and deep voids of Gpc scale as required to fit the distance redshift relations of SNe.