A new approach to the analysis of the phase space of f(R)-gravity

TL;DR

This paper introduces a novel dynamical system method for analyzing f(R)-gravity cosmologies, simplifying the phase space study and providing new insights into fixed points related to inflation and dark energy.

Contribution

The paper presents a new formalism that avoids complex inversions and links fixed points to scale factors with physical interpretation in f(R) models.

Findings

New method simplifies phase space analysis of f(R) gravity.

Application to inflationary and dark energy models demonstrates effectiveness.

Provides physical meaning to fixed points via scale factors.

Abstract

We propose a new dynamical system formalism for the analysis of f(R) cosmologies. The new approach eliminates the need for cumbersome inversions to close the dynamical system and allows the analysis of the phase space of f(R)-gravity models which cannot be investigated using the standard technique. Differently form previously proposed similar techniques, the new method is constructed in such a way to associate to the fixed points scale factors, which contain four integration constants (i.e. solutions of fourth order differential equations). In this way a new light is shed on the physical meaning of the fixed points. We apply this technique to some f(R) Lagrangians relevant for inflationary and dark energy models.