Linear perturbations in spherically symmetric dust cosmologies including a cosmological constant

TL;DR

This paper investigates the behavior of linear perturbations in spherically symmetric dust cosmologies with a cosmological constant, revealing that coupling effects are generally negligible but can be significant in certain void models.

Contribution

It introduces a numerical method to analyze gauge-invariant perturbations in inhomogeneous cosmologies including a cosmological constant, highlighting the coupling effects and their impact.

Findings

Coupling effects are negligible within cosmic variance limits.

Strong coupling effects are present in certain void models.

The method allows for deriving initial variables and computing angular power spectra.

Abstract

We study the dynamical behaviour of gauge-invariant linear perturbations in spherically symmetric dust cosmologies including a cosmological constant. In contrast to spatially homogeneous FLRW models, the reduced degree of spatial symmetry causes a non-trivial dynamical coupling of gauge-invariant quantities already at first order perturbation theory and the strength and influence of this coupling on the spacetime evolution is investigated here. We present results on the underlying dynamical equations augmented by a cosmological constant and integrate them numerically. We also present a method to derive cosmologically relevant initial variables for this setup. Estimates of angular power spectra for each metric variable are computed and evaluated on the central observer's past null cone. By comparing the full evolution to the freely evolved initial profiles, the coupling strength will be determined for a best fit radially inhomogeneous patch obtained in previous works (see Redlich et. al. (2014)). We find that coupling effects are not noticeable within the cosmic variance limit and can therefore safely be neglected for a relevant cosmological scenario. On the contrary, we find very strong coupling effects in a best fit spherical void model matching the distance redshift relation of SNe which is in accordance with previous findings using parametric void models.