We consider $f(R,T)$ modified theories of gravity in the context of string-theory-inspired dilaton gravity. We deal with a specific model that under certain conditions describes the late time Universe in accord with observational data in modern cosmology and addresses the $H_0$ tension. This is done by exploring the space of parameters made out of those coming from the modified gravity and dilatonic charge sectors. We employ numerical methods to obtain several important observable quantities.

In the present work, we study cosmology in dilatonic $f(R,T)$ gravity to address the inflationary phase of the early universe. As usual, in dilatonic gravity, the scalar potential assumes the exponential form. However, this potential is not good enough to be in accordance with the Planck 2018 data. More strikingly, the generalized $\beta$-exponential cannot take this into account either. It is just only presence of the dilatonic sector, in the intermediate coupling regime, that can help the theory to be in full accordance with the observational data.

We consider $f(R,T)$ modified theories of gravity in the context of string theory inspired dilaton gravity. We deal with a specific model that under certain conditions describes the late time Universe in accord with observational data in modern cosmology and addresses the $H_0$ tension. This is done by exploring the space of parameters made out of those coming from the modified gravity and dilatonic charge sectors. We employ numerical methods to obtain several important observable quantities.

In the present work we study cosmology in dilatonic $f(R,T)$ gravity to address the inflationary phase of the early Universe. As usual, in dilatonic gravity the scalar potential assumes the exponential form. However, this potential is not good enough to be in accord with the Planck 2018 data. More strikingly, the generalized $β$-exponential cannot take this into account either. It is just the presence of the dilatonic sector, in the intermediate coupling regime, that can help the theory to be in full accord with the observational data.