Reheating constraints on an inflation model with nonminimal derivative coupling in the light of Planck 2018 data

Reheating is a process by which the inflaton's energy density transfers to conventional matter after cosmic inflation. Currently, there is no cosmic observational evidence to directly detect the reheating era, but it may impose additional constraints on inflationary models. Depending upon the model, e-folding number during reheating Nre and the final reheating temperature Tre, as well as its effective equation of state parameter omega(re), may be directly linked to the inflation observables such as the scalar spectral index ns and the tensor-to-scalar ratio r. By restricting the values of the effective equation of state parameter observationally, one can derive more stringent limits on inflationary models than those obtained from other routes. In this paper, we are interested to consider the reheating era in an inflation model with a nonminimal derivative coupling of the scalar field to impose some severe constraints on the parameter space of the model in the light of Planck 2018 data. We study the reheating final temperature and e-folds number in terms of the scalar spectral index and omega(re) within a numerical analysis on the model's parameter space. To realize a viable range of the reheating equation of state parameter in this nonminimal derivative inflation model, we obtain some observationally acceptable subspaces in the N-re - omega(re) phase plane. To this end, we consider some sort of polynomial potentials to obtain some constraints on the model's parameter space which corresponds to viable values of the scalar spectral index and tensor-to-scalar ratio released by Planck 2018 TT+TE+EE+LowE observational data. Finally, we compare the obtained constraints in this nonminimal set-up with those derived from a single, minimally coupled scalar field inflation model to reveal the physics of the reheating in the context of nonminimal derivative inflation model.