Constraining the Deviation of Kerr Metric via Bumpy Parameterization and Particle Swarm Optimization in Extreme Mass-Ratio Inspirals

TL;DR

The study tackles testing general relativity in the strong-field regime by constraining Kerr deviations in extreme mass-ratio inspirals using a bumpy Kerr parameter $\delta \tilde{Q}$. It integrates particle swarm optimization (PSO) with a reduced-dimensionality likelihood built from a Bumpy-AK waveform, enabling efficient global searches in a high-dimensional space (15D, effectively reduced to 9D for optimization). A key finding is that the Bumpy-AK likelihood is highly multimodal, producing tens of thousands of SIPs and STPs; ensemble averaging over SIP/STP populations mitigates systematic biases in phase-coupled parameters, at the cost of increased variance in sky localization. The work highlights the necessity of accounting for degeneracies not captured by Fisher analyses and provides a pathway toward robust EMRI data-analysis pipelines for future space-borne gravitational-wave missions.

Abstract

Measurement of deviations in the Kerr metric using gravitational wave (GW) observations will provide a clear signal of new Physics. Previous studies have developed multiple parameterizations (e.g. ``bumpy" spacetime) to characterize such deviations in extreme mass ratio inspirals (EMRI) and employed analyses based on the Fisher information matrix (FIM) formalism to quantify the constraining power of space-borne GW detectors like LISA and Tianqin, e.g., achieving a constraint sensitivity levels of $10^{-4} \sim 10^{-2}$ on the dimensionless bumpy parameter $δ\tilde{Q}$ under varying source configurations in analytical kluge waveform for LISA. In this paper, we advance prior analyses by integrating particle swarm optimization (PSO) with matched filtering under a restricted parameter search range to enforce a high probability of convergence for PSO. Our results reveal a significant number of degenerate peaks in the likelihood function over the signal parameter space with values that exceed the injected one. This extreme level of degeneracy arises from the involvement of the additional bumpy parameter $δ\tilde{Q}$ in the parameter space and introduces systematic errors in parameter estimation. We show that these systematic errors can be mitigated using information contained in the ensemble of degenerate peaks, thereby restoring the reliability of astrophysical inferences about EMRI systems from GW observations. This study highlights the critical importance of accounting for such degeneracies, which are absent in FIM-based analyses, and points out future directions for improving EMRI data analysis.