Constraining viscous fluid models in $f(Q)$ gravity with data

We investigate the impact of bulk viscosity on the accelerating expansion and large-scale structure formation of a Universe in which the underlying gravitational interaction is described by $f(Q)$ gravity. Various paradigmatic choices of the $f(Q)$ gravity theory, including power-law, exponential, and logarithmic models, are considered. To test the cosmological viability of these $f(Q)$ gravity models, we use {the Baryon Acoustic Oscillations ($BAO$) measurements from the Dark Energy Spectroscopic Instrument (DESI) Survey, cosmic chronometers ($CC$) from Hubble measurements, the SNIa distance moduli measurements from the PantheonP + SH0ES, growth rate ($f$-data), and redshift-space distortions ($f\sigma_8$) datasets, the latter two once the linear cosmological perturbations, growth rate $f(z)$, and redshift-space distortion $f\sigma_8(z)$ are studied. Thus, we perform the combined analyses for: PantheonP + SH0ES, PantheonP + SH0ES + f, and PantheonP + SH0ES + $f\sigma_8$. We compute the best-fit values $\Omega_m$, $H_0\,\mathrm{(km/s/Mpc)}$, $r_d$, $M_{abs}$, $\gamma$, $\sigma_8$, $n$, $p$ and $\Gamma$ including the bulk viscosity coefficient $\zeta$. Through a detailed statistical analysis, based on the Akaike Information Criterion (AIC) and Bayesian / Schwartz Information Criterion (BIC), a statistical comparison of the $f(Q)$ gravity models with $\Lambda$CDM is made. Among the three $f(Q)$ models, only the non-viscous $f(Q)$ power-law model yields robust parameter estimates and substantial observational support without any outright rejections. In contrast, both exponential and logarithmic $f(Q)$ models (with or without bulk viscosity) are rejected by multiple model selection criteria.