The cosmology in f(R,T) gravity without dark energy

We examine the evolution of universe in $f(R,T)$ gravity where $R$ is the Ricci curvature and $T$ is the trace of energy momentum tensor. We focus on the specific form $f(R,T) = R+f(T)$ and explicitly find out the relation between $f(T)$ and state of equation $w$ by adiabatic condition. All possible modes of evolution of the scale factor for the five kinds of state of equation, $w= \pm 1, \pm 1/3, 0$ are exhibited. We simulate numerically the plots of redshift versus distance modulus for three interesting modes and then obtain the good fitting curve compared with the astronomical observation data.