The Multi-parameter Test of Gravitational Wave Dispersion with Principal Component Analysis

Abstract

In this work, we consider a conventional test of gravitational wave (GW) propagation which is based on the phenomenological parameterized dispersion relation to describe potential departures from General Relativity (GR) along the propagation of GWs. But different from tests conventionally performed previously, we vary multiple deformation coefficients simultaneously and employ the principal component analysis (PCA) method to remedy the strong degeneracy among deformation coefficients and obtain informative posteriors. The dominant PCA components can be better measured and constrained, thus are expected to be more sensitive to potential departures from the waveform model. Using this method we analyze 10 selected events and get the result that the combined posteriors of the dominant PCA parameters are consistent with GR within 3-$σ$ uncertainty. The standard deviation of the first dominant PCA parameter is 3 times smaller than that of the original dispersion parameter of the leading order. However, the multi-parameter test with PCA is more sensitive to not only potential deviations from GR but also systematic errors of waveform models. the difference in results obtained by using different waveform templates indicates that the demands of waveform accuracy are higher to perform the multi-parameter test with PCA.