G\"{o}del solution in $f(R,T)$ gravity

In this paper we study G\"{o}del universe in the framework of $f(R,T)$ modified theories of gravity, where $R$ is the curvature scalar and $T$ the trace of the energy momentum tensor. We demonstrate that G\"{o}del solution occurs in this modified theory and still we suggest a path to understanding the smallness of the cosmological constant.