Cosmological phase space of generalized hybrid metric-Palatini theories of gravity

TL;DR

This paper analyzes the cosmological dynamics of generalized hybrid metric-Palatini gravity theories using a phase space approach, identifying fixed points, solution classes, and comparing with observational data.

Contribution

It formulates an autonomous system for these theories, finds fixed points for different functions, and explores solution behaviors including static universes.

Findings

No global attractors exist in the system.

Two classes of scale factor solutions are identified.

Numerical solutions align with current cosmological observations.

Abstract

Using a dynamical system approach we study the cosmological phase space of the generalized hybrid metric-Palatini gravity theory, characterized by the function $f\left(R,\mathcal R\right)$, where $R$ is the metric scalar curvature and $\mathcal R$ the Palatini scalar curvature of the spacetime. We formulate the propagation equations of the suitable dimensionless variables that describe FLRW universes as an autonomous system. The fixed points are obtained for four different forms of the function $f\left(R,\mathcal R\right)$, and the behavior of the cosmic scale factor $a(t)$ is computed. We show that due to the structure of the system, no global attractors can be present and also that two different classes of solutions for the scale factor $a(t)$ exist. Numerical integrations of the dynamical system equations are performed with initial conditions consistent with the observations of the cosmological parameters of the present state of the Universe. In addition, using a redefinition of the dynamic variables, we are able to compute interesting solutions for static universes.