Late-time acceleration in $f\left( Q\right) $ gravity: Analysis and constraints in an anisotropic background

This paper is devoted to investigate the anisotropic locally rotationally symmetric (LRS) Bianchi type-I space-time in the context of the recently proposed $f(Q)$ gravity in which $Q$ is the non-metricity scalar. For this purpose, we consider a linear form of $f\left( Q\right)$ gravity model, specifically, $f\left( Q\right) =\alpha Q+\beta$, where $\alpha$ and $$ are free parameters and we analyzed the exact solutions of LRS Bianchi type-I space-time. The modified Friedmann equations are solved by presuming an expansion scalar $\theta \left( t\right)$ is proportional to the shear scalar $\sigma \left( t\right)$ which leads to the relation between the metric potentials as $A=B^{n}$ where $n$ is an arbitrary constant. Then we constrain our model parameters with the observational Hubble datasets of 57 data points. Moreover, we discuss the physical behavior of cosmological parameters such as energy density, pressure, EoS parameter, and deceleration parameter. The behavior of the deceleration parameter predicts a transition from deceleration to accelerated phases in an expanding Universe. Finally, the EoS parameter indicates that the anisotropic fluid behaves like the standard $\Lambda$CDM model.