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

TL;DR

This paper introduces a minimal higher-order correction to the quadratic inflation model, which aligns its predictions with CMB data and modifies reheating dynamics, demonstrating the importance of controlled deformations in simple inflationary theories.

Contribution

The paper presents a simple field redefinition that minimally deforms quadratic inflation, making it compatible with observational data and affecting reheating properties.

Findings

Corrected potential yields n_s ≈ 0.965 and r ≈ 0.036, consistent with Planck 2018.

Reheating equation of state slightly softer, w_reh ≈ -0.011, compared to matter-like regime.

Reheating temperature increases by a factor of about 3.4 with the correction.

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.