A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories

TL;DR

This paper generalizes Kasner transition rules in bouncing Bianchi I cosmologies within modified gravity theories, providing a geometric interpretation and explicit solutions, advancing understanding of anisotropic universe evolution through non-singular bounces.

Contribution

It introduces a unified transition rule for Kasner exponents in various modified gravity models and offers a geometric framework for anisotropy evolution during bounces.

Findings

Transition rules as linear maps in the Kasner plane

Equivalence of anisotropy evolution to particle motion on a sphere

Explicit solution for Bianchi I with ekpyrotic matter

Abstract

We derive transition rules for Kasner exponents in bouncing Bianchi I models with generic perfect fluid matter fields for a broad class of modified gravity theories where cosmological singularities are resolved and replaced by a non-singular bounce. This is a generalization of results obtained previously in limiting curvature mimetic gravity and loop quantum cosmology. A geometric interpretation is provided for the transition rule as a linear map in the Kasner plane. We show that the general evolution of anisotropies in a Bianchi I universe -- including during the bounce phase -- is equivalent to the motion of a point particle on a sphere, where the sphere is the one-point compactification of the Kasner plane. In addition, we study the evolution of anisotropies in a large family of bouncing Bianchi I space-times. We also present a novel explicit solution to the Einstein equations for a Bianchi I universe with ekpyrotic matter with a constant equation of state $\omega=3$.