Bulk viscous cosmological model in $f(R,T)$ theory of gravity

In this paper, we have presented bulk viscous cosmological model of the universe in the modified gravity theory in which the Lagragian of the gravitational action contains a general function $f(R, T) $, where $R$ and $T$ denote the curvature scalar and the trace of the energy-momentum tensor respectively, in the framework of a flat Friedmann-Robertson-Walker model with isotropic fluid. We obtain cosmological solution in $f(R,T)$ theory of gravity, specially of particular choice $f(R,T)=R+2\lambda T$, where $\lambda$ is a constant, in the presence of bulk viscosity that are permitted in Eckart theory, Truncated Israel Stewart theory and Full Israel Stewart theory. The physical and geometrical properties of the models in Eckart, Truncated Israel Stewart theory and Full Israel Stewart theory are studied in detail. The analysis of the variation of bulk viscous pressure, energy density, scale factor, Hubble parameter and deceleration parameter with cosmic evolution are done in the respective theories. The models are analyzed by comparison with recent observational data. The cosmological models are compatible with observations.