On the validity of the perturbative description of axions during inflation

TL;DR

The paper addresses whether axions coupled to gauge fields can consistently generate sizable tensor modes during inflation without breaking perturbation theory. It develops proper counting rules within the in-in formalism for resonantly enhanced gauge fields, showing that naive real-part counting overestimates loop growth due to cancellations between phases. Parametric perturbativity bounds are derived, yielding $ξ \lesssim 3.5$ (and $ξ \lesssim 4.4$ from explicit 1-loop), with additional non-Abelian constraints that depend on the gauge group and loop factors. The results significantly constrain the viability of synthetic tensor generation via axion-gauge couplings, particularly in natural-inflation-like scenarios, though certain tunings (e.g., axion decay during inflation) could evade some non-Gaussianity constraints. Overall, the work provides robust perturbativity criteria that any axion-gauge-field inflation model must satisfy to remain reliable.

Abstract

Axions play a central role in many realizations of large field models of inflation and in recent alternative mechanisms for generating primordial tensor modes in small field models. If these axions couple to gauge fields, the coupling produces a tachyonic instability that leads to an exponential enhancement of the gauge fields, which in turn can decay into observable scalar or tensor curvature perturbations. Thus, a fully self-consistent treatment of axions during inflation is important, and in this work we discuss the perturbative constraints on axions coupled to gauge fields. We show how the recent proposal of generating tensor modes through these alternative mechanisms is in tension with perturbation theory in the in-in formalism. Interestingly, we point out that the constraints are parametrically weaker than one would estimate based on naive power counting of propagators of the gauge field. In the case of non-Abelian gauge fields, we derive new constraints on the size of the gauge coupling, which apply also in certain models of natural large field inflation, such as alignment mechanisms.

Figures (7)

• Figure 1: Gauge field 2-point function $\left< AA \right>$
• Figure 2: 1-loop correction to $\left< AA \right>$
• Figure 3: Scalar (or tensor) 2-point function $\left< \zeta \zeta \right>$ ($\left<h h\right>$)
• Figure 4: 1-loop correction to $\left< \zeta \zeta \right>$ (or $\left< h h \right>$)
• Figure 5: The thick, blue line shows the ratio of the numerical 1-loop calculation of $\left\langle AA \right\rangle$ divided by the tree level calculation (the result for $\left\langle A'A' \right\rangle$ is very slightly larger). The thin, red line shows the parametric estimate using \ref{['sec:parameric-est']}, which is considerably more restrictive than the result from the numerical 1-loop calculation. \ref{['sec:details-1-loop']}.