Viscous Fluid Cosmology in Symmetric Teleparallel Gravity

In this manuscript, we analyze the viscous fluid cosmological model in framework of recently proposed $f(Q)$ gravity by assuming three different forms bulk viscosity coefficients, specifically, $(i)\zeta =\zeta_{0}+\zeta_{1}\left( \frac{\dot{a}}{a}\right) +\zeta_{2}\left( \frac{{\ddot{a}}}{\dot{a}}\right) $, $(ii)\zeta \frac{\dot{a}}{a}\right)$, and $(iii)\zeta =\zeta_{0}$ a linear model, particularly, $f(Q)=\alpha Q$ where $\alpha \neq 0$ is free parameter. We estimate coefficients parameter values using combined H(z)+Pantheon+BAO data set. study asymptotic behavior our utilizing phase space method. find that corresponding to all cases, depicts evolution universe from matter dominated decelerated epoch (a past attractor) stable de-sitter accelerated future attractor). Further, physical effective pressure, equation state (EoS), statefinder parameters. pressure component presence shows negative EoS predicts expansion for cases. Moreover, obtain trajectories lie quintessence region it converges $\Lambda$CDM fixed point far future. deSitter like comes purely $\bar{\zeta}_0$ case without any geometrical modification GR. late-time cases are identical.