Multiparameter tests of general relativity using principal component analysis with next-generation gravitational wave detectors

TL;DR

This paper demonstrates how Principal Component Analysis can optimize tests of general relativity using next-generation gravitational wave detectors, enabling precise constraints on deviations from GR with improved sensitivity.

Contribution

It introduces a PCA-based method to identify the best linear combinations of PN parameters for testing GR with advanced detectors like CE and ET.

Findings

CE can measure dominant combinations to better than 10% accuracy.

ET outperforms CE in certain mass ranges due to better low-frequency sensitivity.

PCA parameters' sensitivity varies with total mass and PN deformation parameters.

Abstract

Principal Component Analysis (PCA) is an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing fractional deformation parameters. We use PCA to construct the `best-measured' linear combinations of the PN deformation parameters from the data. This helps to set stringent limits on deviations from GR and detect possible beyond-GR physics. In this paper, we study the effectiveness of this method with the proposed next-generation gravitational wave detectors, Cosmic Explorer (CE) and Einstein Telescope (ET). Observation of compact binaries with total masses between 20-200 $\mathrm{M}_{\odot}$ in the detector frame and at a luminosity distance of 500 Mpc, CE can measure the three most dominant linear combinations to an accuracy better than 10%, and the most dominant one to better than 0.1%. For specific ranges of masses and linear combinations, constraints from ET are better by a few factors than CE. This improvement is because of the improved low frequency sensitivity of ET compared to CE (between 1-5 Hz). In addition, we explain the sensitivity of the PCA parameters to the different PN deformation parameters and discuss their variation with total mass. We also discuss a criterion for quantifying the number of most dominant linear combinations that capture the information in the signal up to a threshold.