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-Robertson-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 )∝e^t (motivated by the de Sitter solution); and two types of power-law expansion with a (t )∝t^{1 /2} and a (t )∝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 (R ,T ) associated with the scalar-field potentials of the representation used are deduced.