# Efficient self-resonance instability from axions

## TL;DR

This paper analyzes the parametric resonance instability of axion fields, especially the flapping resonance, using Floquet analysis and Hill's equation, revealing conditions for significant gravitational wave emission.

## Contribution

It introduces a new parameter $ ilde{q}$ to classify resonance types and extends the analysis beyond harmonic oscillations to anharmonic cases.

## Key findings

- Flapping resonance leads to the strongest mode growth.
- Resonance instability depends on the parameter $ ilde{q}$.
- The study clarifies conditions for resonance in cosine potentials.

## Abstract

It was recently shown that a coherent oscillation of an axion can cause an efficient parametric resonance, leading to a prominent emission of the gravitational waves (GWs). In this paper, conducting the Floquet analysis, we investigate the parametric resonance instability, which potentially triggers the emission of the GWs from axions. Such a resonance instability takes place, when the time evolution of the background field significantly deviates from the harmonic oscillation. Therefore, the resonance instability cannot be described by the Mathieu equation, whose stability/instability chart is well known. In this paper, introducing an explicitly calculable parameter $\tilde{q}$, which can be used to classify different types of the parametric resonance described by the general Hill's equation, we investigate the stability/instability chart for the general Hill's equation. This can also apply to the case where the background oscillation is anharmonic. We show that the flapping resonance instability, which takes place for $\tilde{q}=O(1)$, typically leads to the most significant growth of the inhomogeneous modes among the self-resonance instability. We also investigate whether the flapping resonance takes place for the cosine potential or not.