Inflation and reheating predictions in polynomial inflation with small and large fields

We explore the inflationary dynamics and reheating predictions of the fourth-order generalized polynomial inflation model featuring adjustable saddle-point position and flatness near the saddle point for both small and large field cases, based on the latest Planck 2018 Cosmic Microwave Background (CMB) and BICEP/Keck data. We observe that the small field case, with saddle points proximate to the origin, exhibits a significantly lower tensor-to-scalar ratio compared to the large field case. Additionally, the spectral index of the curvature perturbation increases as the flatness near the potential saddle point decreases. Through an analysis of the interplay between inflation and reheating parameters derived from the expansion history of the pivot CMB scale, we establish a permissible range for the reheating parameters. We find that both the small and large cases of polynomial inflation can be consistent with the latest observations due to potential flatness reduction, except for the case where the saddle point deviates significantly from the origin, and the reheating process accentuates the disparities in parameter space between small and large field inflationary scenarios.