Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals

TL;DR

This paper explores how extreme mass-ratio inspirals can test Lorentz symmetry breaking in bumblebee gravity, showing that LISA can constrain the symmetry-breaking parameter to very tight levels.

Contribution

It develops EMRI waveforms in bumblebee gravity and demonstrates how LISA observations can constrain Lorentz symmetry breaking parameter $ ext{l}$.

Findings

Lorentz symmetry breaking parameter $ ext{l}$ significantly affects EMRI waveforms.

Waveform modifications grow with $ ext{l}$ and orbital eccentricity.

LISA can constrain $ ext{l}$ to an uncertainty of order 10^{-4}.

Abstract

Extreme mass-ratio inspirals (EMRIs), with their long-lived and highly relativistic orbital evolution, can probe strong-field spacetime geometry and provide an important means to test general relativity. In this work, we investigate EMRI waveforms in a Schwarzschild-like black hole spacetime arising in bumblebee gravity, where Lorentz symmetry breaking (LSB) is characterized by a dimensionless parameter $\ell$. We construct EMRI waveforms within the Augmented Analytic Kludge (AAK) framework using the modified orbital frequencies and fluxes. We find that $\ell$ significantly affects the orbital evolution and thereby modifies the waveform. These modifications grow with increasing $\ell$ and are further enhanced for more eccentric orbits. Furthermore, using Bayesian analysis, we obtain the posterior distributions of EMRI with the parameter $\ell$ included. Our results show that all injected source parameters are recovered within their $1\,\sigma$ credible intervals. We find that the bumblebee parameter $\ell$ can be constrained with an uncertainty of order $\mathcal{O}(10^{-4})$ by LISA.