PREPRINT
9B24A780-6145-4C12-9D39-4D70A8EC3C9E

# Cosmology in $f\left(Q\right)$ gravity: A unified dynamical system analysis at background and perturbation levels

Wompherdeiki Khyllep, Jibitesh Dutta, Emmanuel N. Saridakis, Kuralay Yesmakhanova
arXiv:2207.02610

Submitted on 6 July 2022

## Abstract

Motivated by the fact that cosmological models based on $f\left(Q\right)$ 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 $f\left(Q\right)$ 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 $\mathrm{\Lambda }$CDM 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 $f\left(Q\right)$ gravity can be considered as a very promising alternative to the $\mathrm{\Lambda }$CDM concordance model.

## Preprint

Comment: 10 pages and 8 figs. We welcome comments

Subjects: General Relativity and Quantum Cosmology; Astrophysics - Cosmology and Nongalactic Astrophysics; High Energy Physics - Theory