Isocurvature-Free QCD Axion Dark Matter from Inflaton-Driven Early QCD: the Necessity of Inflationary Plateaus

Abstract

A direct coupling between the inflaton and Standard Model gluons can dynamically raise the QCD confinement scale during inflation, making the axion temporarily heavy and suppressing axion isocurvature perturbations. As inflation proceeds, the confinement scale relaxes, the axion becomes light, and late-time de Sitter fluctuations can generate the observed dark matter abundance. We analyze this mechanism without specifying an inflationary potential, instead parametrizing the background by $\epsilon(N) \propto 1/N^p$, where $N$ is the number of $e$-folds before the end of inflation. The single parameter $p$ distinguishes monomial models ($p=1$), standard plateau models ($p=2$), and ultra-flat plateau or hilltop-like models ($p\ge 3$). We analytically show that the mechanism selects plateau-like ($p\ge 2$) inflation: monomial models generically cause the confinement scale to grow too rapidly, while plateau models keep the QCD sector under perturbative control. In the minimal scenario, reheating occurs through the same inflaton-gluon coupling, and viable axion dark matter production is obtained when deconfinement occurs after the CMB window. The early-confinement sector also generically shifts the scalar spectral index to smaller, redder values. Because ultra-flat ($p \ge 3$) models inherently predict overly red spectra, this shift exacerbates their tension with CMB data, leaving $p=2$ plateau models as the phenomenologically viable parameter space (in this parametrization).