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 $a(t)\propto e^t$ (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 $f(R,T)$ associated with the scalar-field potentials of the representation used are deduced.

• Received 5 December 2021
• Accepted 11 February 2022

DOI:https://doi.org/10.1103/PhysRevD.105.064019