Testing the bulk viscosity within the f(R,T) gravity in light of DESI-DR2 observations

Abstract

We investigate the cosmological implications of the bulk viscosity within the framework of $f(R,T)$ gravity by considering the linear model $f(R,T)=R+2\lambda T$, where $\lambda$ characterizes the matter--geometry coupling. Assuming a homogeneous and isotropic Friedmann--Lema\^{i}tre--Robertson--Walker Universe, we derive analytical expressions for the Hubble parameter in two different scenarios: model A, corresponding to a pressureless viscous fluid ($\omega=0$), and model B, where the equation of state (EoS) parameter is treated as a free parameter. The cosmological parameters are constrained through a Markov Chain Monte Carlo analysis. The results show that both viscous $f(R,T)$ models provide an excellent description of the current expansion history and remain compatible with the combined observational data. Model A is slightly favored over the standard cosmological model ($\Lambda$CDM) according to AICc, reflecting the improved fit achieved with only one additional free parameter. In contrast, the BIC continues to favor the simpler $\Lambda$CDM model owing to its stronger penalty on model complexity. Although model B yields the lowest minimum $\chi^2$, the improvement is too small to justify the introduction of an additional free parameter, resulting in a statistical performance comparable to $\Lambda$CDM according to the AICc but less favorable according to the BIC.