Viability of the $R+e^T$ cosmology

We propose a new theoretical approach for a cosmological model, which starts from an exponential of the trace of the energy-momentum tensor-dependence on the gravitational action, to be summed to the Ricci scalar. We derive the referred field equations and Friedmann-like equations. We derive the scale factor, Hubble parameter and deceleration parameter, in terms of both time and redshift. In possession of those parameters in terms of the redshift, we confront their predictions with the observational Hubble dataset and the outcomes are pretty satisfactory so that the model can be seen as a new alternative to the cosmological constant problem. We also present the statefinder diagnostic and discuss profoundly the dynamical behaviour of the model.