Universal Constraints on Axions from Inflation

TL;DR

This paper demonstrates that the generation of curvature perturbations via an axion-like particle with axial coupling has a universal form independent of the axion being the inflaton, imposing constraints on inflationary models involving axions.

Contribution

It shows that the axial coupling mechanism for curvature perturbation generation is universal and cannot produce observable tensor modes without additional fields or conditions.

Findings

Curvature perturbation generation is universal and unaffected by the axion's role as inflaton.

Generating large tensor modes via this mechanism is not feasible without violating constraints.

Constraints from slow-roll evolution limit axion-based inflationary models.

Abstract

We consider the presence of an axion like particle, $\sigma$, with a generic $CP$ violating axial coupling of the form $ (\alpha \, \sigma/f) F \tilde{F}$, where $F_{\mu\nu}$ is the gauge field strength of a generic abelian $U(1)$ gauge group, not necessarily associated with the standard electromagnetism, and $f$ is the decay constant of the axion. It has previously been demonstrated that if the axion is identified with the inflaton, such an interaction can lead to measurable cosmological signatures (non-Gaussian modifications of the curvature perturbation spectrum) depending on the parameter $\xi= \alpha \dot{\sigma}/ (f H)$. In the present paper we will show that the generation of curvature perturbation at horizon crossing due to the axial coupling has a universal form and remains unmodified in terms of the $\xi$ parameter even if the axion, $\sigma$, is not identified with the inflaton. As a consequence, it does not appear to be possible to generate CMB tensor perturbations through this mechanism, larger than the vacuum ones, without violating the observational constraints unless we combine this mechanism with a curvaton or if the $\sigma$ field becomes heavy and decays during inflation. Even in this last case there are non-trivial constraints coming from the slow-roll evolution of the curvature perturbation on super horizon scales which should be taken into account. We also comment on implications for inflationary models where axions play an important role as, for example, models of natural inflation where more than one axion are included and models where the curvaton is an axion.