A transition from a decelerated to an accelerated phase of the universe   expansion from the simplest non-trivial polynomial function of T in the   f(R,T) formalism
  In this work we present cosmological solutions from the simplest non-trivial $T$-dependence in $f(R,T)$ theory of gravity, with $R$ and $T$ standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Although such an approach yields a highly non-linear differential equation for the scale factor, we show that it is possible to obtain analytical solutions for the cosmological parameters. For some values of the free parameters, the model is able to predict a transition from a decelerated to an accelerated expansion of the universe. 
P. H. R. S. Moraes, G. Ribeiro, R. A. C. Correa
hep-th