A dynamical system analysis of hybrid metric-Palatini cosmologies

TL;DR

This paper uses dynamical system techniques to analyze the cosmological solutions of hybrid metric-Palatini gravity models, identifying fixed points corresponding to different universe evolutions, including accelerating and static solutions.

Contribution

It introduces a dynamical system framework to study $f(X)$ hybrid metric-Palatini gravity cosmologies, revealing new accelerating solutions and stability properties of static and bouncing universes.

Findings

Identification of fixed points representing power-law and de Sitter expansions

Discovery of new attractor solutions with acceleration

Analysis of stability for Einstein static and bouncing solutions

Abstract

The so called $f(X)$ hybrid metric-Palatini gravity presents a unique viable generalisation of the $f(R)$ theories within the metric-affine formalism. Here the cosmology of the $f(X)$ theories is studied using the dynamical system approach. The method consists of formulating the propagation equation in terms of suitable (expansion-normalised) variables as an autonomous system. The fixed points of the system then represent exact cosmological solutions described by power-law or de Sitter expansion. The formalism is applied to two classes of $f(X)$ models, revealing both standard cosmological fixed points and new accelerating solutions that can be attractors in the phase space. In addition, the fixed point with vanishing expansion rate are considered with special care in order to characterise the stability of Einstein static spaces and bouncing solutions.