Bianchi $VII_A$ solutions of quadratic gravity

TL;DR

This paper explores exact numerical solutions in quadratic gravity models, showing that small initial anisotropies in the universe do not grow indefinitely, indicating weak isotropisation tendencies.

Contribution

It provides numerical solutions for anisotropic quadratic gravity models and analyzes their asymptotic behaviors, including de Sitter and flat space, highlighting stability features.

Findings

Solutions asymptote to de Sitter, flat space, or singularity.

Small anisotropies do not grow indefinitely, suggesting weak isotropisation.

Solutions depend strongly on initial conditions.

Abstract

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model $H^ 3$ for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain way. It is found solutions which asymptote de Sitter space, Riemann flat space and a singularity. The question of isotropisation of an initially anisotropic Universe is of great importance in the context of cosmology. Although isotropisation is not directly discussed in this present work, we show that sufficiently small anisotropies, do not increase indefinitely according to particular quadratic gravity theories. It can be understood as weak isotropisation, and we stress that this result is strongly dependent on initial conditions.