Rolling axions during inflation: perturbativity and signatures

TL;DR

This work analyzes a pseudo-scalar X coupled to gauge fields during inflation, showing that gauge-field amplification can source scalar and tensor perturbations with distinctive features such as chirality and localized spectra. It systematically compares two realizations, X=\phi (inflaton) and X=\sigma (spectator), deriving backreaction and perturbativity bounds using in-in formalism and energy-density estimates. The main finding is that CMB-scale signals from these mechanisms comfortably lie within perturbative control and near-backreaction-free regimes (xi roughly up to 4.6–4.8), while small-scale (GW/PBH) signals push toward the perturbativity boundary, potentially requiring order-one corrections. Overall, the paper strengthens the case that sourced GW signals at CMB scales are viable and distinct from vacuum GWs, while clarifying the limits for smaller-scale applications and debating previous perturbativity conclusions.

Abstract

The motion of a pseudo-scalar field $X$ during inflation naturally induces a significant amplification of the gauge fields to which it is coupled. The amplified gauge fields can source characteristic scalar and tensor primordial perturbations. Several phenomenological implications have been discussed in the cases in which (i) $X$ is the inflation, and (ii) $X$ is a field different from the inflation, that experiences a temporary speed up during inflation. In this second case, visible sourced gravitational waves (GW) can be produced at the CMB scales without affecting the scalar perturbations, even if the scale of inflation is several orders of magnitude below what is required to produce a visible vacuum GW signal. Perturbativity considerations can be used to limit the regime in which these results are under perturbative control. We revised limits recently claimed for the case (i), and we extend these considerations to the case (ii). We show that, in both cases, these limits are satisfied by the applications that generate signals at CMB scales. Applications that generate gravitational waves and primordial black holes at much smaller scales are at the limit of the validity of this perturbativity analysis, so we expect those results to be valid up to possibly order one corrections.

Figures (9)

• Figure 1: Time evolution of the contribution to the gauge field physical energy density from modes with a given comoving momentum $k$. The three different curves correspond to the three approximated solutions (\ref{['colsol']}), (\ref{['bessol']}) and (\ref{['A-simple']}). From early to late times (from right to left), the figure shows the UV-divergent vacuum energy density, the gauge field amplification due its interaction with $X \left( t \right)$, and the dilution due to the expansion of the universe. For definiteness, the constant parameter $\xi = 3$ is assumed.
• Figure 2: Time evolution of the contribution to the gauge field physical energy density from modes with three different comoving momenta. The quantity $x_*$ is the ratio between the physical momentum of the mode and the Hubble rate at the time when $\sigma = \sigma_*$.
• Figure 3: Diagrammatic representation of the one loop terms (\ref{['AA-inin']}) and (\ref{['XX-inin']}). Solid lines denote $\delta X$ modes, while wiggly lines denote vector field $A_+$ modes. The small bullets denote the interaction (\ref{['Hintconspa']}).
• Figure 4: Ratio ${\cal R}_A$ for the $X = \phi$ case, as a function of $\xi$. The ratio is evaluated for a fixed mode (fixed $k$) of the size of the Planck pivot scale (due to approximate scale invariance, nearly the same bound is obtained at smaller scales). The different curves shown correspond to different values of the rescaled time $x \equiv - k \tau$ at which ${\cal R}_A$ is evaluated. For instance $x_{0.1}$ indicates that ${\cal R}_A$ is evaluated when the energy density in that mode is $10\%$ of the peaked value that it had previously assumed (as shown in Figure \ref{['fig:rhoti']}, the energy density in one given mode reaches a peak value, and it then decreases).
• Figure 5: Ratio $R_A$ (left panel) and $R_A$ (right panel) for $\delta = 0.2$ and for varying $\xi_*$. The different lines correspond to different times at which the ratios are evaluated.