Axion Isocurvature Perturbations Survive the Scaling Evolution of Axion Domain Walls

Abstract

We revisit the evolution of axion domain walls seeded by inflationary fluctuations. In our previous work, we showed that such domain-wall networks retain superhorizon correlations even after entering the scaling regime. We extend our previous analysis to the case with large initial fluctuations, where many minima of the axion potential are already populated when the axion starts to oscillate. Although the conventional misalignment contribution can have suppressed long-wavelength isocurvature perturbations when many vacua are averaged over, axions produced by domain-wall collapse provide an additional contribution that can dominate when the walls enter the scaling regime before annihilation. In particular, the biased vacuum energy released during wall annihilation inherits the superhorizon correlations of the inflationary fluctuations and transfers them to the axion energy density. We find that sizable isocurvature perturbations can therefore survive even after the walls annihilate. We also discuss generic isocurvature constraints on dark matter produced by domain-wall collapse.