Cosmology in the novel scalar-tensor representation of $f(R,T)$ gravity

Abstract: We apply cosmological reconstruction methods to the $f(R,T)$ modified gravity, in its recently developed scalar-tensor representation. We do this analysis assuming a perfect fluid in a Friedmann-Lema^{i}tre-Robsertson-Walker (FLRW) universe. In this contribution we show the equations of motion obtained and we present the solutions found for one of the particular cases we analysed: an exponential evolution of the cosmological scale factor.