Singular value decomposition in parametrised tests of post-Newtonian theory

TL;DR

This paper uses Singular Value Decomposition to transform correlated post-Newtonian parameters into independent combinations, improving the accuracy of gravitational wave data analysis for testing gravity theories.

Contribution

It introduces a SVD-based method to decorrelate PN parameters, enhancing the precision of parameter estimation in gravitational wave observations.

Findings

Improved parameter estimation accuracy using SVD

Reduced correlations among PN coefficients

Enhanced potential for testing gravity theories

Abstract

Various coefficients of the 3.5 post-Newtonian (PN) phasing formula of non-spinning compact binaries moving in circular orbits is fully characterized by the two component masses. If two of these coefficients are independently measured, the masses can be estimated. Future gravitational wave observations could measure many of the 8 independent PN coefficients calculated to date. These additional measurements can be used to test the PN predictions of the underlying theory of gravity. Since all of these parameters are functions of the two component masses, there is strong correlation between the parameters when treated independently. Using Singular Value Decomposition of the Fisher information matrix, we remove this correlations and obtain a new set of parameters which are linear combinations of the original phasing coefficients. We show that the new set of parameters can be estimated with significantly improved accuracies which has implications for the ongoing efforts to implement parametrised tests of PN theory in the data analysis pipelines.