The phase space view of f(R) gravity

TL;DR

This paper explores the phase space geometry of flat FLRW models in f(R) gravity, analyzing equilibrium points, stability, and comparing with scalar-tensor theories, introducing new Lagrangians and Hamiltonians.

Contribution

It provides a comprehensive phase space analysis of f(R) gravity models, including stability and new effective Lagrangians and Hamiltonians.

Findings

Identification of equilibrium points and their stability

Comparison between f(R) gravity and scalar-tensor phase spaces

Introduction of new effective Lagrangians and Hamiltonians

Abstract

We study the geometry of the phase space of spatially flat Friedmann-Lemaitre-Robertson-Walker models in f(R) gravity, for a general form of the function f(R). The equilibrium points (de Sitter spaces) and their stability are discussed, and a comparison is made with the phase space of the equivalent scalar-tensor theory. New effective Lagrangians and Hamiltonians are also presented.