Cosmology in scalar-tensor \(f(R,T)\) gravity

In this work, we use reconstruction methods to obtain cosmological solutions in the recently developed scalar-tensor representation of \(f(R,T)\) gravity. Assuming that matter is described by an isotropic perfect fluid and the spacetime is homogeneous and isotropic, i.e., the Friedmann-Lemaître-Robsertson-Walker (FLRW) universe, the energy density, the pressure, and the scalar field associated with the arbitrary dependency of the action in \(T\) can be written generally as functions of the scale factor. We then select three particular forms of the scale factor: an exponential expansion with \({a(t)\propto e^t}\) (motivated by the de Sitter solution); and two types of power-law expansion with \({a(t)\propto t^{1/2}}\) and \({a(t)\propto t^{2/3}}\) (motivated by the behaviors of radiation- and matter-dominated universes in general relativity, respectively). A complete analysis for different curvature parameters \({k=\{-1,0,1\}}\) and equation of state parameters \({w=\{-1,0,1/3\}}\) is provided. Finally, the explicit forms of the functions \(f\left(R,T\right)\) associated with the scalar-field potentials of the representation used are deduced.