# Nonlinear resonant oscillation of gravitational potential induced by ultralight axion in $f(R)$ gravity

## TL;DR

This paper investigates how ultralight axion dark matter causes oscillations in gravitational potential within $f(R)$ gravity, revealing that nonlinear resonance effects could enhance detection prospects via gravitational wave detectors.

## Contribution

It demonstrates that nonlinear resonance between ultralight axions and scalarons in $f(R)$ gravity amplifies gravitational potential oscillations, improving detectability.

## Key findings

- Oscillations of gravitational potential are sensitive to gravity models.
- Nonlinear resonance enhances detection signals.
- Potential for gravitational wave detection of axion-induced oscillations.

## Abstract

We study the ultralight axion dark matter with mass around $10^{-22}$ eV in $f(R)$ gravity which might resolve the dark energy problem. In particular, we focus on the fact that the pressure of the axion field oscillating in time produces oscillations of gravitational potentials. We show that the oscillation of the gravitational potential is sensitive to the model of gravity. Remarkably, we find that the detectability of the oscillation through the gravitational wave detectors can be significantly enhanced due to the nonlinear resonance between the ultralight axion and the scalaron.