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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 theRicci scalar and trace of the energy-momentum tensor, respectively. Althoughsuch an approach yields a highly non-linear differential equation for the scalefactor, we show that it is possible to obtain analytical solutions for thecosmological parameters. For some values of the free parameters, the model isable to predict a transition from a decelerated to an accelerated expansion ofthe universe.

astrophysics and space science

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