Reviving Quadratic Inflation: Minimal Deformation for CMB Compatibility and Reheating Consistency

Abstract

We revisit the quadratic inflationary potential by introducing a minimal higher-order correction obtained through a simple field redefinition, leading to the potential V(chi) = (1/2) m^2 * (chi - (gamma/14) * chi^7)^2. While the uncorrected quadratic model predicts n_s approximately 0.967 and r approximately 0.13, in strong tension with CMB data, the corrected potential yields n_s approximately 0.965 and r approximately 0.036, fully consistent with Planck 2018 constraints. Beyond inflationary observables, the deformation also impacts the reheating phase. In the quadratic case, reheating corresponds to a matter-like regime with w_reh = 0, whereas the corrected potential gives w_reh approximately -0.011, a slightly softer equation of state. This modification raises the reheating temperature by a factor of about 3.4 (for N_reh = 10), or equivalently extends the reheating duration at fixed temperature. Our results demonstrate that even a minimal higher-order correction is sufficient to reconcile the quadratic model with observations while providing a more consistent post-inflationary history, highlighting the relevance of controlled deformations of simple inflationary scenarios.