Universal Constraints on Axions from Inflation

TL;DR

This work analyzes axion-like particles with a CP-violating $α σ/(4f) F_{μν} \tilde{F}^{μν}$ coupling during inflation and demonstrates that the resulting curvature perturbation sourcing is universally governed by the parameter $ξ=\frac{α \dot{σ}}{2 f H}$, regardless of whether the axion is the inflaton. Through gauge-field production and one-loop corrections, the authors show that attempts to boost tensor modes inevitably induce sizable scalar non-Gaussianity unless the axion decays rapidly or the perturbations are generated via a curvaton mechanism, yielding strong constraints on $ξ$ (roughly $ξ \lesssim 3$) and on tensor-to-scalar ratios. The analysis uses two gauges to establish a universal interaction between curvature perturbations and gauge fields, showing that gravity couples these sectors in a way that cannot be easily decoupled. Consequently, models with natural inflation or multiple axions must respect stringent bounds on decay constants and on isocurvature-curvature mixing, with superhorizon evolution further limiting scenarios where axions source large primordial tensors. The results have broad implications for constructing inflationary models with axions, including curvaton scenarios and N-flation-like setups.

Abstract

We consider the presence of an axion like particle, $σ$, with a generic $CP$ violating axial coupling of the form $ (α\, σ/f) F \tilde{F}$, where $F_{μν}$ 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 $ξ= α\dotσ/ (f H)$. 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 $ξ$ parameter even if the axion, $σ$, 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 $σ$ 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.

Figures (1)

• Figure 1: Feynman diagrams associated with the one-loop contribution to the 2 and 3 point function of the scalar curvature and to the 2 point function of the tensor curvature