Stable Isotropic Cosmological Singularities in Quadratic Gravity

TL;DR

This paper demonstrates that in quadratic gravity theories, isotropic cosmological singularities are stable against small inhomogeneities, with a specific isotropic solution acting as a stable attractor near the initial singularity, unlike in general relativity.

Contribution

It shows the stability of isotropic singularities in quadratic gravity and identifies a specific solution as a stable attractor, extending previous results beyond general relativity.

Findings

Isotropic singularities are stable in quadratic gravity.

A specific isotropic solution is the stable attractor near the singularity.

The results support the universality of this attractor in various cosmological models.

Abstract

We show that, in quadratic lagrangian theories of gravity, isotropic cosmological singularities are stable to the presence of small scalar, vector and tensor inhomogeneities. Unlike in general relativity, a particular exact isotropic solution is shown to be the stable attractor on approach to the initial cosmological singularity. This solution is also known to act as an attractor in Bianchi universes of types I, II and IX, and the results of this paper reinforce the hypothesis that small inhomogeneous and anisotropic perturbations of this attractor form part of the general cosmological solution to the field equations of quadratic gravity. Implications for the existence of a 'gravitational entropy' are also discussed.