Eur. Phys. J. C (2024) 84: 310
https://doi.org/10.1140/epjc/s10052-024-12549-4

Regular Article - Theoretical Physics

Cosmological constraints on $f(Q)$ gravity with redshift space distortion data

¹ Laboratory of Physics of Matter and Radiations, Mohammed I University, BP 717, Oujda, Morocco
² Higher School of Education and Training, Mohammed I University, BP 717, Oujda, Morocco

^a dalale.mhamdi@ump.ac.ma

Received: 29 November 2023
Accepted: 11 February 2024
Published online: 24 March 2024

Abstract

In this paper, we explore one of Einstein’s alternative formulations which involves the non-metricity scalar, Q, within the framework of f(Q) theory. Our study focuses on solving the modified Friedmann equations for the case of dust matter, $\rho ={\rho }_m$, and a form of $f(Q)=\alpha +\beta Q^n$. We investigate the behavior of our model in both linear $(n=1)$ and nonlinear $(n\ne 1)$ scenarios at the background and perturbation levels. By employing the Markov chain Monte Carlo (MCMC) method, we constrain our model using observational datasets including redshift space distortion, cosmic chronometers, and Pantheon${}^{+}$. Without using any parameterization of the growth rate index which quantifies the deviation from the $\mathrm{\Lambda }$CDM model, both models exhibit good accuracy in describing the redshift space distortion. We further analyze the dynamics of the Universe using cosmography parameters, where our model exhibits a phase transition between deceleration and acceleration phases at $z=0.789$. Our findings reveal that our model exhibits a phantom-like behavior based on statefinder diagnostic analysis. Interestingly, the model demonstrates a rich variety of behaviors, resembling either a quintessence-like scenario for $(n<1)$ or phantom-like scenario for $(n\ge 1)$. Using the MCMC best fit and parameterizing the growth index, the evolution of the growth index also depends on the parameter n, either remaining constant (in the linear case) or showing a decreasing trend (in the nonlinear case), indicating a weaker growth rate of density perturbations during earlier cosmic times. Finally, we compare our findings of the growth index with the values obtained in the literature.