Observational evidence of bulk viscosity effects in f(R,T) cosmological models

In this study, we explore an $f(R,T)$ cosmological model incorporating bulk viscosity, focusing on scenarios where the matter sector is minimally and linearly coupled to the geometry, specifically $f(R,T)=R+2\lambda T$, with λ as the coupling constant. Two cases of bulk viscosity are examined: Case I with a time-dependent coefficient $\zeta ={\zeta }_0+{\zeta }_{1}H$ (${\zeta }_1\ne 0$) and Case II with a constant viscosity $\zeta ={\zeta }_0$ (${\zeta }_1=0$). By employing Bayesian methods, including MCMC techniques, we constrain the model parameters $H_0$, λ, ${\zeta }_0$, and ${\zeta }_1$ using the Hubble $H\left(z\right)$ and Pantheon+SH0ES datasets. Our analysis reveals a transition from a decelerating to an accelerating universe driven by bulk viscosity. Case I exhibits a present-day deceleration parameter $q_0=-0.51$, indicating moderate acceleration, while Case II shows a slightly stronger acceleration with $q_0=-0.53$. The evolution of the energy density ρ and effective pressure $\overline{p}$ aligns with standard cosmological expectations, with positive energy density and consistently negative effective pressure, characteristic of DE. Furthermore, the effective equation of state parameter ${\omega }_{eff}$ and the $Om\left(z\right)$ diagnostic suggest quintessence-like behavior, with the violation of the strong energy condition supporting the observed accelerated expansion of the universe. These findings suggest that the $f(R,T)$ model with bulk viscosity offers a consistent and plausible description of late-time cosmic acceleration, aligning well with observational data.