Paramerization of deceleration parameter in $f(Q)$ gravity

Abstract

In this article, we investigate the modified symmetric teleparallel gravity or $f(Q)$ gravity, where $Q$ is the non-metricity, to study the evolutionary history of the universe by considering the functional form of $f(Q)=\alpha Q^n$, where $\alpha$ and $n$ are constants. Here, we consider the parametrization form of the deceleration parameter as $q=q_0+\frac{q_1\,z}{(1+z)^2}$ which provides the desired property for sign flip from a decelerating to an accelerating phase. We get the solution of the Hubble parameter by examining the mentioned parametric form of $q$, and then we impose the solution in Friedmann equations. Employing the Bayesian analysis for the Observational Hubble data (OHD), we estimated the constraints on the associated free parameters $(H_0,q_0,q_1)$ to determine if this model may challenge the $\Lambda$CDM limitations. Furthermore, the constrained current value of the deceleration parameter $q_0=-0.832^{+0.091}_{-0.091}$ shows that the present universe is accelerating. We also investigate the evolutionary trajectory of energy density, pressure, and EoS parameters to conclude the accelerating behavior of the universe. Finally, we try to demonstrate that the considered parametric form of the deceleration parameter is compatible with $f(Q)$ gravity.