Confronting general relativity with principal component analysis: Simulations and results from GWTC-3 events

TL;DR

This paper develops and validates a PCA-based, multiparameter test of general relativity (GR) in the gravitational-wave inspiral by compressing eight fractional PN deviation parameters into a small set of principal components. Implemented within the TIGER and FTI frameworks, the method uses a Bayesian, data-driven approach to derive event-specific PCA parameters and combines information across events to constrain deviations from GR. Through extensive zero-noise injections, GR and non-GR signals, eccentric NR injections, and a multi-event analysis of GWTC-3 sources, the study demonstrates that the leading PCA components reliably test GR and that mis-modeling (e.g., neglecting eccentricity or precession) can produce apparent violations. The joint analysis of GWTC-3 events yields no statistically significant GR deviations, confirming the method’s sensitivity and robustness while highlighting areas for future improvement and extension to higher PN orders and other null tests.

Abstract

We present a comprehensive assessment of multiparameter tests of general relativity (GR) in the inspiral regime of compact binary coalescences using principal component analysis (PCA). Our analysis is based on an extensive set of simulated gravitational-wave (GW) signals, including both general relativistic and non-GR sources, injected into zero-noise data colored by the noise power spectral densities of the LIGO and Virgo GW detectors at their designed sensitivities. We evaluate the performance of PCA-based methods in the context of two established frameworks: TIGER and FTI. For GR-consistent signals, we find that PCA enables stringent constraints on potential deviations from GR, even in the presence of multiple free parameters. Applying the method to simulated signals that explicitly violate GR, we demonstrate that PCA is effective at identifying such deviations. We further test the method using numerical relativity waveforms of eccentric binary black hole systems and show that missing physical effects--such as orbital eccentricity--can lead to apparent violations of GR if not properly included in the waveform models used for analysis. Finally, we apply our PCA-based test to selected real gravitational-wave events from GWTC-3, including GW190814 and GW190412. We present joint constraints from selected binary black hole events in GWTC-3, finding that the 90% credible bound on the most informative PCA parameter is $0.03^{+0.08}_{-0.08}$ in the TIGER framework and $-0.01^{+0.05}_{-0.04}$ in the FTI framework, both of which are consistent with GR. These results highlight the sensitivity and robustness of the PCA-based approach and demonstrate its readiness for application to future observational data from the fourth observing runs of LIGO, Virgo, and KAGRA.

Figures (10)

• Figure 1: Posteriors of $\delta\hat{\phi}^{(1)}_{\rm PCA}$ (upper panel) and $\delta\hat{\phi}^{(2)}_{\rm PCA}$ (lower panel) for each simulated injection—listed in Table \ref{['tab:table_gr_inj_aligned_spin']} and discussed in Sec. \ref{['sec:align_spin_inj']}—with the left and right panels displaying results from BBHs with detector-frame total masses of $25 M_{\odot}$ and $60 M_{\odot}$, respectively. In each violin plot, the colored horizontal bars and the horizontal white solid line denote the 90% credible intervals and the posterior median, respectively. We mark the GR value of zero with dashed gray lines.
• Figure 2: Posterior distributions of $\delta\hat{\phi}^{(1)}_{\rm PCA}$ (left panel) and $\delta\hat{\phi}^{(2)}_{\rm PCA}$ (right panel) for each simulated precessing-spin GR injection---listed in Table \ref{['tab:table_gr_inj_precess_spin']} and discussed in Sec. \ref{['subsec:prec_gr_injs']}---presented as violin plots. The colored and white horizontal bars have the same meaning as in Fig. \ref{['fig:gr_inj_aligned_spin']}. For all the binary configurations, both the PCA parameters are consistent with the GR value (dashed gray line) of 0.
• Figure 3: Posterior distributions of the dominant two PCA parameters ($\delta\hat{\phi}^{(1)}_{\rm PCA}$, top row; $\delta\hat{\phi}^{(2)}_{\rm PCA}$, bottom row) obtained from GR-consistent injections based on GW151226-, GW190412-, and GW190814-like BBH systems, as described in Sec. \ref{['subsec:prec_HM_inj']}. The left panel compares PCA posteriors for GW151226-like injections at network SNRs of 20 and 40, using IMRPhenomXPHM for injection and its parametrized version for recovery. The right panel compares aligned-spin (IMRPhenomXHM for injection and its parametrized version for recovery) and precessing (IMRPhenomXPHM for injection and its parametrized version for recovery) injections for GW190412-like and GW190814-like systems. The colored and white horizontal bars have the same meaning as in Fig. \ref{['fig:gr_inj_aligned_spin']}. In all cases, the PCA constraints are consistent with the GR value of 0, marked by the dashed gray line.
• Figure 4: Violin plots showing the posteriors of $\delta \hat{\phi}^{(1)}_{\rm PCA}$ and $\delta \hat{\phi}^{(2)}_{\rm PCA}$ from the GR-consistent aligned-spin injection analysis within the FTI framework, using the SEOBNRv4$\textunderscore$ROM (x-label:1) and SEOBNRv4HM$\textunderscore$ROM (x-label:2) waveform models for GW150914-like BBH systems, as listed in entries 1 and 2 of Table \ref{['tab:table_gr_inj_fti']} and discussed in Sec. \ref{['sec:FTI_inj']}. The horizontal bars have the same meaning as in Fig. \ref{['fig:gr_inj_aligned_spin']}. In every case, the PCA posteriors remain consistent with the GR prediction of zero, indicated by the dashed gray line.
• Figure 5: Violin plots showing the posteriors of $\delta \hat{\phi}^{(1)}_{\rm PCA}$ and $\delta \hat{\phi}^{(2)}_{\rm PCA}$ from the GR-consistent precessing-spin injection analysis within the FTI framework, as presented in entries 3 and 4 of Table \ref{['tab:table_gr_inj_fti']} and discussed in Sec. \ref{['sec:FTI_inj']}. GR-consistent GW signals are simulated using the IMRPhenomXPHM waveform model, and parameter estimation is performed using the parametrized SEOBNRv4HM$\textunderscore$ROM model. The horizontal bars have the same meaning as in Fig. \ref{['fig:gr_inj_aligned_spin']}. The median values of the PCA parameter posteriors show notable deviations from zero in all cases. Specifically, for the strongly precessing binary configuration, the GR value is excluded from the 90% credible interval of the $\delta \hat{\phi}^{(2)}_{\rm PCA}$ posterior.