Exact Friedmann Solutions in Higher-Order Gravity Theories

TL;DR

This paper derives exact solutions for homogeneous, isotropic cosmological models in higher-order gravity theories, revealing diverse evolutionary behaviors and attractor solutions in vacuum and perfect fluid cases.

Contribution

It provides explicit, exact solutions for fourth-order gravity theories in cosmology, including vacuum and perfect fluid models, with analysis of their early and late-time behaviors.

Findings

Solutions include closed, open, and flat geometries in vacuum cases.

All perfect fluid solutions are spatially flat.

Multiple solutions with the same matter and topology exhibit diverse evolution.

Abstract

We find the general behaviour of homogeneous and isotropic cosmological models in some fourth-order theories of gravity. Explicit, exact, general solutions are given for both empty universes and those filled with a perfect fluid. For the vacuum case, solutions are found with closed, open and flat geometries, whilst the perfect fluid solutions are all spatially flat. Both early and late-time limits are studied, and attractor behaviour towards simple power-law expansion is identified. Multiple solutions to the same theories, with the same matter content and topology are found. It is shown that these solutions exhibit great variety in their evolution.