Cosmological constraints in symmetric teleparallel gravity with bulk viscosity

In this study, we explore the accelerated expansion of the universe within the framework of modified $f(Q)$ gravity. The investigation focus on the role of bulk viscosity in understanding the universe's accelerated expansion. Specifically, a bulk viscous matter-dominated cosmological model is considered, with the bulk viscosity coefficient expressed as $\zeta= \zeta_0 \rho H^{-1} + \zeta_1 H$. We consider the power law $f(Q)$ function $f(Q)=\alpha Q^n$, where $\alpha$ and $n$ are arbitrary constants and derive the analytical solutions for the field equations corresponding to a flat FLRW metric. Subsequently, we used the combined Cosmic Chronometers (CC)+Pantheon+SH0ES sample to estimate the free parameters of the obtained analytic solution. We conduct Bayesian statistical analysis to estimate the posterior probability by employing the likelihood function and the MCMC random sampling technique, along with the AIC and BIC statistical assessment criteria. In addition, we explore the evolutionary behavior of significant cosmological parameters. The effective equation of state (EOS) parameter predicts the accelerating behavior of the cosmic expansion phase. Further, by the statefinder and $Om(z)$ diagnostic test, we found that our viscous model favors quintessence-type behavior and can successfully describe the late-time scenario.