In the near future, space-borne gravitational wave (GW) detector LISA can open the window of low-frequency band of GW and provide new tools to test gravity theories.
In this work, we consider multi-parameter tests of GW generation and propagation where the deformation coefficients are varied simultaneously in parameter estimation and principal component analysis (PCA) method are used to transform posterior samples into new bases for extracting the most informative components. The dominant components can be better constrained and more sensitive to potential departures from general relativity (GR).
We extend previous works by employing Bayesian parameter estimation and performing not only null tests but also tests with injections of subtle GR-violated signals.
We also apply the multi-parameter test with PCA in the phenomenological parameterized test of GW propagation.
Our work complements previous works and further demonstrates the enhancement provided by PCA method.
Considering a supermassive black hole binary system as GW source, we find that $1\sigma$ bounds of the most dominant PCA parameter can be one order of magnitude tighter than the bounds of original deformation parameter of leading order of frequency. The departures around $1\sigma$ in original parameters can yield departures more than $10\sigma$ in the most dominant PCA parameters.