Cosmography of the f(R,T) gravity theory

Currently, in order to explain the accelerated expansion phase of the universe, several alternative approaches have been proposed, among which the most common are dark energy models and alternative theories of gravity. Although these approaches rest on very different physical aspects, it has been shown that both are in agreement with the data in the current status of cosmological observations, thus leading to an enormous degeneration between these models. So until evidences of higher experimental accuracy are available, more conservative model independent approaches are a useful tool for breaking this degenerated cosmological models picture. Cosmography as a kinematic study of the universe is the most popular candidate on this regard. Here we show how to construct the cosmographic equations for the f (R, T ) theory of gravity within a conservative scenario of this theory, where R is the Ricci curvature scalar and T is the trace of the energy-moment tensor. Such equations relate f(R,T) and its derivatives at the current time t0 to the cosmographic parameters q0, j0 and s0. In addition, we show how these equations can be written within different dark energy scenarios, thus helping to discriminate between them. We also show how different f(R,T) gravity models can be constrained using these cosmographic equations.