Stochastic isocurvature constraints for axion dark matter with high-scale inflation

TL;DR

This paper uses a stochastic formalism to accurately compute axion isocurvature perturbations during high-scale inflation, revealing viable dark matter scenarios that previous linear methods overlooked due to non-perturbative effects.

Contribution

It introduces a stochastic spectral expansion approach to model non-linear axion dynamics, expanding the understanding of isocurvature constraints at high inflationary scales.

Findings

Identifies a significant parameter window where axions can be dark matter without violating constraints.

Shows non-perturbative effects dominate the isocurvature spectrum in key regions.

Demonstrates the inadequacy of linear approximations in certain high-scale inflation scenarios.

Abstract

Axions are among the best motivated dark matter candidates. Their production in the early Universe by the vacuum misalignment mechanism gives rise to isocurvature perturbations, which are constrained by cosmic microwave background measurements. In this paper, we compute the axion isocurvature power spectrum using spectral expansion in the stochastic Starobinsky-Yokoyama formalism, which captures non-linear effects in the axion dynamics. In contrast to most of the existing literature, we focus on high inflationary Hubble rates of order $10^{13}~{\rm GeV}$, and demonstrate that there is a significant window in which axions can account for all or part of the dark matter abundance without violating the isocurvature bounds or tensor mode bounds. Crucially, we find that the isocurvature spectrum is dominated by non-perturbative contributions in a large part of this window. Therefore the commonly used linear approximation is not reliable in this region, making the stochastic approach essential.