Axion inflation in the regime of homogeneous backreaction

TL;DR

This work investigates the SGWB from axion inflation with a Chern-Simons coupling to gauge fields, focusing on the regime where backreaction is captured by a homogeneous inflaton. It develops a perturbative formalism for tensor and scalar sourced perturbations under homogeneous backreaction and explores how the GW spectrum depends on the inflaton-gauge coupling and potential slope. Through an explicit example and parameter scans, it shows that a detectable SGWB with multiple peaks is possible within regions where the gradient energy remains subdominant, but the results are highly parameter-sensitive and can fail when gradient energy grows, as revealed by recent lattice simulations. The study provides a practical framework for predicting SGWB signatures and guiding observations (PTA, astrometry, interferometers), while highlighting the necessity of full lattice analyses to validate predictions in the strong-gradient regime.

Abstract

We investigate the Stochastic Gravitational Wave Background (SGWB) produced in models of axion inflation coupled to gauge fields. Achieving a detectable signal at Pulsar Timing Array, astrometry, or interferometer frequencies requires a sufficiently strong amplification of the gauge fields, at a level that induces significant backreaction on the inflaton background dynamics. Numerical studies based on the approximation of homogeneous backreaction (i.e., neglecting inhomogeneities of the inflaton field) exhibit oscillations in the inflaton velocity, with corresponding peaks in the SGWB spectrum. The most recent lattice simulations have questioned the validity of this regime, showing examples characterized by a rapid increase in the inflaton gradient energy and the breakdown of homogeneous backreaction. We compute this energy density perturbatively within the assumption of homogeneous backreaction, obtaining examples with a detectable SGWB and with an inflaton gradient energy that remains subdominant to the inflaton zero-mode kinetic energy throughout inflation.

Figures (9)

• Figure 1: Evolution as a function of the number of e-folds of various contributions to the energy density. From top to bottom (referring to the left portion of the figure): the dominant (orange) curve is the potential energy of the inflaton; the second (blue) curve is the kinetic energy of the inflaton zero mode; the third (magenta) curve is the energy density in gauge fields; the fourth (red) curve is the gradient energy density of the inflaton perturbations; the fifth (green) curve is the GW energy density. The (black) vertical dashed line indicates the moment at which the gradient energy of the inflaton perturbations becomes equal to the kinetic energy of the zero mode.
• Figure 2: The figure shows the fractional energy density of the vacuum (nearly horizontal black dashed curve) and sourced (dominant blue and subdominant red curve for the left and red helicities, respectively) SGWB, computed under the assumption of homogeneous backreaction, compared to the sensitivity of various observatories. The shaded region beyond the vertical dashed line represents the frequency spectrum produced after the breakdown of the homogeneous backreaction approximation.
• Figure 3: Results for a flatter inflaton potential in the intermediate region (slope $v'=-0.1516$ rather than $-0.2822$), while all the other parameters coincide with those of the 'baseline' model that was used in the two previous figures. Left panel: evolution of the parameter $\xi$ controlling the gauge‑field amplification. Central panel: evolution of various energy density components. Right panel: present GW fractional energy density. The main difference with the results in Figure \ref{['fig:EnergyDensities_57_495']} is that now the inflaton spatial gradient energy remains significantly smaller than the kinetic energy for the whole evolution.
• Figure 4: Results for a decreased inflaton-gauge interaction with respect to the 'baseline' model (${\tilde{f}}^{-1} = 22$ rather than $57$), while the potential is unchanged. The panels are organized as in the previous figure.
• Figure 5: Results for an increased inflaton-gauge interaction (${\tilde{f}}^{-1} = 80$ for the top row and $75$ for the bottom row, in contrast to $57$ in the "baseline" model) and flatter potential in the intermediate region (slope $v' = -0.1237$ for the top row and $-0.1129$ for the bottom row, in contrast to $-0.2822$ in the "baseline" model). The panels are organized as in the two previous figures.