Cosmological dynamics of fourth order gravity: A compact view

TL;DR

This paper develops a phase space framework for analyzing flat FLRW cosmologies in f(R) gravity, revealing complex evolutionary paths including inflation, matter domination, and late-time acceleration.

Contribution

It introduces a compact phase space approach for f(R) theories, enabling detailed analysis of cosmological dynamics with non-negative Ricci scalar.

Findings

Identification of inflationary, radiation-like, matter-dominated, and de Sitter phases.

Demonstration of possible cosmological evolutions in R + α R^n gravity.

Insights into stability and transitions between different cosmological epochs.

Abstract

We construct a compact phase space for flat FLRW spacetimes with standard matter described by a perfect fluid with a barotropic equation of state for general f(R) theories of gravity, subject to certain conditions on the function f. We then use this framework to study the behaviour of the phase space of Universes with a non-negative Ricci scalar in R + {\alpha}R^n gravity. We find a number of interesting cosmological evolutions which include the possibility of an initial unstable power-law inflationary point, followed by a curvature fluid dominated phase mimicking standard radiation, then passing through a standard matter (CDM) era and ultimately evolving asymptotically towards a de-Sitter-like late-time accelerated phase.