Axion inflation in the strong-backreaction regime: decay of the Anber-Sorbo solution

TL;DR

This paper investigates the stability of the Anber-Sorbo solution in axion inflation with gauge fields, revealing it is unstable and thus challenging previous assumptions about its role in inflationary dynamics.

Contribution

The study provides the first numerical analysis starting from strong backreaction, demonstrating the instability of the Anber-Sorbo solution using multiple analytical and numerical methods.

Findings

The Anber-Sorbo solution is unstable in the strong-backreaction regime.

Previous numerical attempts to reach the AS solution from weak backreaction are inconsistent with its instability.

Multiple methods confirm the absence of a basin of attraction for the AS solution.

Abstract

Axion inflation coupled to Abelian gauge fields via a Chern-Simons-like term of the form $\phi F\tilde{F}$ represents an attractive inflationary model with a rich phenomenology, including the production of magnetic fields, black holes, gravitational waves, and the matter-antimatter asymmetry. In this work, we focus on a particular regime of axion inflation, the so-called Anber-Sorbo (AS) solution, in which the energy loss in the gauge-field production provides the dominant source of friction for the inflaton motion. We revisit the AS solution and confirm that it is unstable. Contrary to earlier numerical works that attempted to reach the AS solution starting from a regime of weak backreaction, we perform, for the first time, a numerical evolution starting directly from the regime of strong backreaction. Our analysis strongly suggests that, at least as long as one neglects spatial inhomogeneities in the inflaton field, the AS solution has no basin of attraction, not even a very small one that might have been missed in previous numerical studies. Our analysis employs an arsenal of analytical and numerical techniques, some established and some newly introduced, including (1) linear perturbation theory along the lines of arXiv:2209.08131, (2) the gradient expansion formalism (GEF) developed in arXiv:2109.01651, (3) a new linearized version of the GEF, and (4) the standard mode-by-mode approach in momentum space in combination with input from the GEF. All these methods yield consistent results confirming the instability of the AS solution, which renders the dynamics of axion inflation in the strong-backreaction regime even more interesting than previously believed.