Cosmology in f (Q) gravity: A unified dynamical systems analysis of the background and perturbations

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 matter-dominated 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 f sigma 8, we find that the models fit observational data successfully, obtaining a behavior similar to that of the Lambda cold dark matter (ACDM) 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.