Axion Inflation with a Massive Abelian Gauge Field

Abstract

An axial coupling between an inflaton and an Abelian gauge field can trigger the tachyonic amplification of one gauge-field helicity. For a massless vector, modes with physical momentum $k/a\sim |\xi |H$ are enhanced by approximately $\exp (\pi |\xi |)$, and sufficiently efficient production can provide substantial friction for the homogeneous inflaton. We extend this mechanism to a vector of mass $m$. The instability is present only for $|\xi |>\bar{m}\equiv m/H$, and in the heavy regime the mode amplitude scales as $\exp [\pi (|\xi |-\bar{m})]$. Because the amplified modes remain well inside the Hubble radius when $\bar{m}\gg 1$, their contribution to long-wavelength curvature perturbations is power-law suppressed at fixed background backreaction. In the weak-backreaction regime we obtain ${\mathcal{P}}_{\zeta }^{\mathrm{id}}\propto {\bar{m}}^{-2}$, while including the gauge-induced friction of scalar perturbations gives the scaling ${\mathcal{P}}_{\zeta }^{\mathrm{id}}\propto {\bar{m}}^{-3}$. These estimates indicate that ${\mathcal{P}}_{\zeta }^{\mathrm{id}}\lesssim 10^{-9}$ on CMB scales should be compatible with gauge field backreaction for $\bar{m}$ larger than order a few hundred. We test the analytical mode functions and backreaction estimates with the first lattice simulations based on a massive-vector extension of the \texttt{Pencil Code}, including simulations in the strongly backreacting regime.

Comments: 52 pages, 11 figures, 1 table, 5 appendices