Density growth in Kantowski-Sachs cosmologies with cosmological constant

TL;DR

This paper investigates how density perturbations evolve in Kantowski-Sachs cosmologies with a positive cosmological constant, analyzing the effects of anisotropy and cosmic bounces through covariant formalisms.

Contribution

It provides a novel analysis of density growth in anisotropic Kantowski-Sachs models with a cosmological constant using gauge-invariant methods.

Findings

Density gradients often reach a local maximum near the cosmic bounce.

Anisotropy influences the evolution of density perturbations.

The study combines analytical and numerical approaches for comprehensive insights.

Abstract

In this work the growth of density perturbations in Kantowski-Sachs cosmologies with a positive cosmological constant is studied, using the 1+3 and 1+1+2 covariant formalisms. For each wave number we obtain a closed system for scalars formed from quantities that are zero on the background and hence are gauge-invariant. The solutions to this system are then analyzed both analytically and numerically. In particular the effects of anisotropy and the behaviour close to a bounce in the cosmic scale factor are considered. We find that typically the density gradient in the bouncing directions experiences a local maximum at or slightly after the bounce.