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

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.
Comment: 11 pages, 3 figures; Contribution to the Sixteenth Marcel Grossman Conference (MG16, Rome, July, 2021), to be published by World Scientific; based on arXiv:2112.02541 [gr-qc]