Quintessence Behaviour of an Anisotropic Bulk Viscous Cosmological Model in Modified $f(Q)$-Gravity

Abstract

In this article, we have discussed the results of our investigation. We consider an anisotropic viscous cosmological model of (LRS) Bianchi type I spacetime universe filled with a viscous fluid under $f(Q)$ gravity. We have studied the modified $f(Q)$ gravity with quadratic form $f(Q)=\alpha Q^2+\beta$, where $Q$ is called as a non-metricity scalar and $\alpha$, $\beta$ are positive constants. We obtain the modified Einstein field equation by considering the viscosity coefficient $\xi (t)={\xi }_{0}H$ and obtained the scale factor $a(t)=2sinh\left(\frac{m+2}{6}\sqrt{\frac{{\xi }_0}{\alpha (2m+1)}}t\right)$.We applied the observational constraint on the apparent magnitude $m(z)$ using the ${\chi }^2$ test formula with observational data set like JLA or Union 2.1 compilation and obtained the best approximate values of the model parameters $m,\alpha ,H_0{\xi }_0$. We have analyzed our model and found a transit phase quintessence anisotropic accelerating universe. We also examined the bulk viscosity equation of state (EoS) parameter ${\omega }_v$ and obtained its current value as ${\omega }_v<-1/3$, which shows the dark energy dominant model, cosmological constant, phantom, and super-phantom dark energy models, and tends to the $\Lambda$CDM value (${\omega }_v=-1$) in the late time. We also estimate the current age of the universe as $t_0\approx 13.6$ Grys and analyze the Statefinder parameters with $(s,r)\to (0,1)$ as $t\to \infty$.

arXiv comment19 pages, 14 figures

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