Narrow Results

This paper deals with an anisotropic cosmological model in the modified theory of $f(Q)$-gravity filled with bulk-viscosity fluid. We investigated the modified $f(Q)$-gravity with quadratic form $f(Q)=-\alpha Q^2$, where $Q$ is the non-metricity scalar and $\alpha$ is a positive constant, in Locally-Rotationally Symmetric (LRS) Bianchi type-$I$ space time universe. We have solved the modified Einstein’s field equations with bulk-viscosity factor $\xi (t)={\xi }_{0}H+{\xi }_1{H}^2$ and obtained average scale factor $a(t)=k_0{[e^{k_{1}t}\mathrm{\text{sech}}(k_{2}t)]}^3$ where $k_0$ is a constant and $k_1=\frac{{\xi }_1{(m+2)}^2}{108\alpha (2m+1)}$, and $k_2=-\frac{(m+2)\sqrt{{\xi }_1{(m+2)}^2+48\alpha {\xi }_0(2m+1)}}{108\alpha (2m+1)}$. We have investigated the model in two cases ${\xi }_0=0$ and ${\xi }_1=0$. We have found the best-fit values of model parameters with observational datasets like Union 2.1 compilation and Joint Light Curve Analysis (JLA) datasets by applying $R^2$-test formula in curve-fitting. Using these best-fit values of model parameters, we have studied the cosmological parameter like Hubble parameter $H$ and deceleration parameter $q$, equation of state (EoS) parameter, age of the present universe $t_0$, etc. We have obtained a transit model (i.e. decelerating to accelerating in current) in the first case ${\xi }_0=0$ and a transit phase model from accelerating to decelerating in the second case ${\xi }_1=0$. We have investigated the EoS parameter ${\omega }_v$ for bulk-viscosity and obtained the present values as $-1.2<{\omega }_v<2.5$, which is supported by the observational results. We have also analyzed energy conditions and statefinder parameters and found that our model approaches to LCDM model in the future.