On stability of the Kasner solution in quadratic gravity

TL;DR

This paper investigates the behavior of a flat anisotropic universe in quadratic gravity near a singularity, revealing conditions under which the universe evolves towards an isotropic state.

Contribution

It demonstrates that quadratic gravity can lead to isotropic singularities from anisotropic initial conditions, expanding understanding of early universe dynamics.

Findings

Existence of a parameter range where singularity becomes isotropic

Identification of regimes with Kasner and vacuum radiation solutions

Numerical evidence supporting isotropization in quadratic gravity

Abstract

We consider dynamics of a flat anisotropic Universe filled by a perfect fluid near a cosmological singularity in quadratic gravity. Two possible regimes are described -- the Kasner anisotropic solution and an isotropic "vacuum radiation" solution which has three sub cases depending on whether the equation of state parameter $w$ is bigger, smaller or equals to $1/3$. Initial conditions for numerical integrations have been chosen near General Relativity anisotropic solution with matter (Jacobs solution). We have found that for such initial conditions there is a range of values of coupling constants so that the resulting cosmological singularity is isotropic.