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-Lemattre-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) alpha e(t) (motivated by the de Sitter solution); and two types of power-law expansion with a(t) alpha t(1/2) and a(t) alpha 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.

Automated summary

In this study, cosmological solutions are obtained in the scalar-tensor representation of f(R, T) gravity using reconstruction methods. By assuming matter as an isotropic perfect fluid and the spacetime as homogeneous and isotropic (Friedmann-Lemattre-Robertson-Walker universe), the energy density, pressure, and scalar field are expressed as general functions of the scale factor. Three particular forms of the scale factor are selected, and a comprehensive analysis is conducted for different curvature and equation of state parameters. The explicit forms of the functions f(R, T) associated with the scalar-field potentials are derived.