Parametrized tests of post-Newtonian theory using principal component analysis

Searching for departures from general relativity (GR) in more than one post-Newtonian (PN) phasing coefficients, called a \emph{multi-parameter test}, is known to be ineffective given the sensitivity of the present generation of gravitational-wave (GW) detectors. Strong degeneracies in the parameter space make the outcome of the test uninformative. We argue that Principal Component Analysis (PCA) can remedy this problem by constructing certain linear combinations of the original PN parameters that are better constrained by gravitational-wave observations. By analyzing binary black hole events detected during the first and second observing runs (O1 and O2) of LIGO/Virgo, we show that the two dominant principal components can capture the essence of a multi-parameter test. Combining five binary black hole mergers during O1/O2, we find that the dominant linear combination of the PN coefficients obtained from PCA is consistent with GR within the 0.38 standard deviation of the posterior distribution. Furthermore, using a set of simulated \emph{non-GR} signals in the three-detector LIGO-Virgo network with designed sensitivities, we find that the method is capable of excluding GR with high confidence as well as recovering the injected values of the non-GR parameters with good precision.