Parametrized tests of post-Newtonian theory using principal component analysis

Understand

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.