Reheating study of Mexican-Hat-type Potentials

Abstract

We study reheating in Mexican Hat type potentials, emphasizing the role of the post-inflationary equation-of-state parameter(${\overline{\ddot{I}‰}}_{\text{re}}$) in shaping observable predictions. By exploring the allowed range of ${\overline{\ddot{I}‰}}_{\text{re}}$, we derive reheating temperature, e-fold counts, and inflationary observables, showing that the conventional Mexican Hat model satisfies Planck18+BK18+BAO constraints on $n_s$ and r. The analysis underscores reheating as a critical link between theoretical potentials and CMB data. In addition, the holographic Mexican Hat realization is examined as a benchmark, with our results mapping its phenomenological boundaries. This work illustrates how reheating studies sharpen constraints and guide refinements of unified inflationary scenarios.