Shear dynamics in Bianchi I cosmologies with R^n-gravity

TL;DR

This paper analyzes shear evolution in Bianchi I cosmologies within R^n gravity, deriving equations, finding exact solutions, and exploring stability and cosmic histories with initial isotropy and subsequent shear anisotropies.

Contribution

It provides a detailed analysis of shear dynamics in Bianchi I models for R^n gravity, including exact solutions and stability analysis based on the parameter n.

Findings

Existence of solutions with initial isotropy and constant shear anisotropies.

Stability of solutions depends on the parameter n.

Characterization of cosmic histories in R^n gravity.

Abstract

We give the equations governing the shear evolution in Bianchi spacetimes for general f(R)-theories of gravity. We consider the case of R^n-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the parameter n. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approaches a constant value.