Cosmography of \(\boldsymbol{f(R,T)}\) Gravity

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 can be in agreement with the data in the current status of cosmological observations, thus leading to an enormous degeneration among these models. Therefore, until evidence of higher experimental accuracy is 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 in this regard. In this paper, 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 the \(f(R,T)\) function and its derivatives at current time \(t_{0}\) to the cosmographic parameters \(q_{0}\), \(j_{0}\), and \(s_{0}\). In addition, we show how these equations can be written within different dark energy scenarios, thus helping to discriminate among them. We also show how different \(f(R,T)\) gravity models can be constrained using these cosmographic equations.