Isocurvature Constraints and Anharmonic Effects on QCD Axion Dark Matter

TL;DR

This paper analyzes how quantum fluctuations of the QCD axion field induce isocurvature perturbations, especially near the potential hilltop, tightening constraints on inflation scale and providing new formulas for perturbation spectra.

Contribution

It extends an analytic method to a time-dependent potential, enabling detailed evolution tracking of axion perturbations and deriving formulas for their power spectrum and non-Gaussianity.

Findings

Isocurvature perturbations are enhanced near the hilltop of the potential.

The inflation scale constraint is tightened to Hinf < 100 GeV for certain axion parameters.

Derived formulas for power spectrum and non-Gaussianity of isocurvature perturbations.

Abstract

We revisit the isocurvature density perturbations induced by quantum fluctuations of the axion field by extending a recently developed analytic method and approximations to a time-dependent scalar potential, which enables us to follow the evolution of the axion until it starts to oscillate. We find that, as the initial misalignment angle approaches the hilltop of the potential, the isocurvature perturbations become significantly enhanced, while the non-Gaussianity parameter increases slowly but surely. As a result, the isocurvature constraint on the inflation scale is tightened as Hinf < O(100) GeV for the axion decay constant fa < 10^10 GeV, near the smaller end of the axion dark matter window. We also derive useful formulae for the power spectrum and non-Gaussianity of the isocurvature perturbations.