On The Existence Of Anisotropic Cosmological Models In Higher-Order Theories Of Gravity

TL;DR

This paper explores anisotropic cosmological solutions in higher-order gravity theories, revealing new vacuum solutions and analyzing their implications for the universe's behavior near the initial singularity.

Contribution

It provides new exact anisotropic vacuum solutions in higher-order gravity theories, extending previous results to a broader class of fourth-order models.

Findings

New anisotropic vacuum solutions analogous to Kasner solutions.

Extended analysis of Bianchi type VIII and IX cosmologies.

Conditions for exponential anisotropic solutions relevant to cosmic no-hair theorems.

Abstract

We investigate the behaviour on approach to the initial singularity in higher-order extensions of general relativity by finding exact cosmological solutions for a wide class of models in which the Lagrangian is allowed to depend nonlinearly upon the three possible linear and quadratic scalars built from the Riemann tensor; $R$, $R_{ab}R^{ab}$ and $R_{abcd}R^{abcd}$. We present new anisotropic vacuum solutions analagous to the Kasner solutions of general relativity and extend previous results to a much wider range of fourth order theories of gravity. We discuss the implications of these results for the behaviour of the more general anisotropic Bianchi type VIII and IX cosmologies as the initial singularity is approached. Furthermore, we also consider the existence conditions for some other simple anisotropic Bianchi I vacuum solutions in which the expansion in each direction is of exponential, rather than power-law behaviour and their relevance for cosmic ``no-hair'' theorems.