Neural Post-Einsteinian Test of General Relativity with the Third Gravitational-Wave Transient Catalog

Abstract

Gravitational waves (GWs) from compact binaries are excellent probes of gravity in the strong- and dynamical-field regime. We report a test of general relativity (GR) with the third GW Transient Catalog (GWTC-3) using the recently developed neural post-Einsteinian framework, both on individual events and at the population level through hierarchical modeling. We find no significant violation of GR and place a constraint that, for the first time, efficiently covers non-GR theories characterized by not only post-Newtonian deviations but also those beyond under the same theory-agnostic framework.

Figures (4)

• Figure 1: Individual-event marginalized posteriors of the npE deviation $|\zeta_b|$ (upper panel) and the theory angle $\varphi$ (lower panel). Observe that all $|\zeta_b|$ posteriors are attached with GR at $\zeta_b=0$, suggesting no significant deviation from GR in general. For $\varphi$, gray dotted lines are added to label the directions of PN dephasings. Observe that the $\varphi$ posteriors mostly peak around the $0$PN direction and the $2$PN direction, which reflects the expected correlation between the npE parameters and the GR parameters through their mutual contribution to the GW phase at these PN orders. Apart from that, no significant preference is found towards those non-PN theory angles (to the left of the $-4$PN line or to the right of the $2$PN line).
• Figure 2: Combined npE constraint using a hierarchical model. The blue contours enclose the 50% and 90% credible regions of a $\vec{\zeta}$ distribution reconstructed from the posterior of the hierarchical inference. The gray dotted lines mark special directions as annotated. Apart from the same PN lines in Fig. \ref{['fig:individual_event_summary']}, we also show the angles where $\varphi$ is defined to be $0$ and $\pi$. For comparison, we take the LVK posteriors published in LIGOScientific:2019fpaLIGOScientific:2020tifLIGOScientific:2021sio and overlay their 90% credible intervals in the npE parameter space as orange lines, whenever the mapping the applicable. Observe that our combined npE constraint is compatible with GR and roughly reproduces the LVK results. Moreover, the npE constraint suggests no significant deviation from GR in the non-PN region, as well as the area "between" integer and half-integer PN orders, where higher PN-order corrections to GR deviations reside Xie:2024ubm.
• Figure 3: Posterior 90% credible contours from individual-event npE analysis assuming a uniform prior over $\zeta_1$ and $\zeta_2$ within the unit circle. Each panel presents the analysis result of an event in Table \ref{['tab:events']}, as suggested by the panel title, and apart from the posterior generated using data of the entire network (black), there are also posteriors generated using data of individual detectors including the Hanford detector (blue), the Livingston detector (orange), and the Virgo detector (green). See Table \ref{['tab:events']} for the list of detectors used in each event. The ticks and labels of the panel axes have been omitted for simplicity. For all panels, the $x$-axis represents $\zeta_1\in[-1,1]$ and the $y$-axis represents $\zeta_2\in[-1,1]$. Each panel is also gridded by gray dotted lines, which are the same PN lines shown in Fig. \ref{['fig:population']} in the main text.
• Figure 4: Hierarchical posterior of the population hyperparameters. The blue contours enclose the 50% and 90% credible regions, respectively.