# Towards a framework for testing general relativity with extreme-mass-ratio-inspiral observations

## TL;DR

This paper develops a computationally efficient Bayesian model selection method for testing general relativity with extreme-mass-ratio-inspiral gravitational wave data, significantly reducing analysis time while maintaining accuracy.

## Contribution

It adapts an evidence-free model selection technique using nested sampling and rethreading to the context of extreme-mass-ratio-inspiral tests of gravity, enabling faster computations.

## Key findings

- Order-of-magnitude computational speed-up over standard nested sampling.
- Robustness of the method demonstrated through benchmarking.
- Effective in synthetic data tests under null hypothesis.

## Abstract

Extreme-mass-ratio-inspiral observations from future space-based gravitational-wave detectors such as LISA will enable strong-field tests of general relativity with unprecedented precision, but at prohibitive computational cost if existing statistical techniques are used. In one such test that is currently employed for LIGO black-hole binary mergers, generic deviations from relativity are represented by $N$ deformation parameters in a generalised waveform model; the Bayesian evidence for each of its $2^N$ combinatorial submodels is then combined into a posterior odds ratio for modified gravity over relativity in a null-hypothesis test. We adapt and apply this test to a generalised model for extreme-mass-ratio inspirals constructed on deformed black-hole spacetimes, and focus our investigation on how computational efficiency can be increased through an evidence-free method of model selection. This method is akin to the algorithm known as product-space Markov chain Monte Carlo, but uses nested sampling and improved error estimates from a rethreading technique. We perform benchmarking and robustness checks for the method, and find order-of-magnitude computational gains over regular nested sampling in the case of synthetic data generated from the null model.