Cosmology in f(Q) gravity: A unified dynamical system analysis at background and perturbation levels

Abstract

Motivated by the fact that cosmological models based on f(Q) gravity are very efficient in fitting observational datasets at both background and perturbation levels, we perform a combined dynamical system analysis of both background and perturbation equations in order to examine the validity of this result through an independent method. We examine two studied f(Q) models of the literature, namely the power-law and the exponential ones. For both cases, we obtain a matterdominated saddle point characterized by the correct growth rate of matter perturbations, followed by the transition to a stable dark-energy dominated accelerated universe in which matter perturbations remain constant. Furthermore, analyzing the behavior of fσ8, we find that the models fit observational data successfully, obtaining a behavior similar to that of ΛCDM scenario, although the exponential model does not possess the latter as a particular limit. Hence, through the independent approach of dynamical systems, we do verify the results of observational confrontation, namely that f(Q) gravity can be considered as a very promising alternative to the ACDM concordance model.