Singular value decomposition in parametrized tests of post-Newtonian theory

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 may measure most of the eight independent PN coefficients calculated to date. These additional measurements can be used to test the PN predictions of the underlying theory of gravity with a similar PN structure. Since all of these parameters are functions of the two component masses, there is a strong correlation between the parameters when treated independently. Using singular value decomposition of the Fisher information matrix, we remove these correlations and obtain a new set of parameters which are a linear combination of the original phasing coefficients. We show that the new set of parameters can be estimated with significantly improved accuracies which have implications for the ongoing efforts to implement parametrized tests of PN theory in the data analysis pipelines.