No Dark Matter Axion During Minimal Higgs Inflation

Abstract

We study minimal versions of Higgs inflation in the presence of a massless QCD axion. While the inflationary energy scale of the metric variant is too high to accommodate isocurvature bounds, it was argued that Palatini Higgs inflation could evade these constraints. We show, however, that an energy-dependent decay constant enhances isocurvature perturbations, implying that axions can at most constitute a tiny fraction $< 10^{-5}$ of dark matter. This conclusion can be avoided in Einstein-Cartan gravity by an additional coupling of the axion to torsion, albeit for a very specific choice of parameters. Analogous constraints as well as the possibility to alleviate them are relevant for all inflationary models with a non-minimal coupling to gravity.

Figures (2)

• Figure 1: Representation of varying decay constant. Since the effective decay constant is reduced during inflation, isocurvature perturbations are enhanced. The dashed line corresponds to the result of Tenkanen:2019xzn, where the change of the decay constant was not taken into account. The physical fluctuation of the axion field is shown with $\delta a$. Figure inspired by Fairbairn:2014zta.
• Figure 2: Representation of a possible way out: If the effective decay constant becomes smaller at lower energy, this improves the isocurvature bound and allows for the axion to account for all of DM. The physical fluctuation of the axion field at low energy is shown with $\delta a_{IR}$. Figure inspired by Fairbairn:2014zta.