Compactifying the state space for alternative theories of gravity

TL;DR

This paper explores the benefits and drawbacks of compactifying the state space in dynamical systems analysis of alternative gravity theories, demonstrating methods with specific cosmological models.

Contribution

It introduces a systematic approach to define compact state spaces for certain gravity models and compares it with non-compact methods in specific cosmological contexts.

Findings

Compact state spaces facilitate analysis of bouncing and recollapsing orbits.

Comparison shows advantages of compactification over non-compact approaches.

Static models are identified within the compactified framework.

Abstract

In this paper we address important issues surrounding the choice of variables when performing a dynamical systems analysis of alternative theories of gravity. We discuss the advantages and disadvantages of compactifying the state space, and illustrate this using two examples. We first show how to define a compact state space for the class of LRS Bianchi type I models in $R^n$-gravity and compare to a non--compact expansion--normalised approach. In the second example we consider the flat Friedmann matter subspace of the previous example, and compare the compact analysis to studies where non-compact non--expansion--normalised variables were used. In both examples we comment on the existence of bouncing or recollapsing orbits as well as the existence of static models.