Testing the strong equivalence principle with multimessenger binary neutron star mergers

Abstract

The constancy of the gravitational constant $G$ is a cornerstone of the strong equivalence principle and of general relativity, yet its possible temporal variation remains a key target in tests of fundamental physics. Gravitational-wave (GW) astronomy, especially when combined with electromagnetic observations, provides an unprecedented new opportunity to probe this principle in the strong-field and dynamical regime. In this work, we develop a GW waveform model with a slowly varying gravitational constant, incorporating its effects both on compact binary dynamics and GW propagation in an expanding universe. Applying this framework to the binary neutron star merger GW170817, together with independent electromagnetic constraints on the luminosity distance, sky localization and binary inclination from GRB 170817A, we perform a joint Bayesian analysis that disentangles varying-$G$ effects from astrophysical degeneracies. We find no evidence for a temporal variation of the gravitational constant, and constrain its fractional time derivative to $\dot{G}/G \in [-3.36 \times 10^{-9}, 5.34\times10^{-10}]~{\rm yr^{-1}}$, representing the most stringent bounds obtained to date from real GW observations. Our results demonstrate the power of multi-messenger astronomy as a precision probe of the strong equivalence principle in the relativistic regime.

Figures (3)

• Figure 1: Posterior distributions from multimessenger constraints on a varying gravitational constant. Posterior distributions of the key parameters are inferred from GW170817 using the TaylorF2 (left) and IMRPhenomXAS_NRTidalv2 (right) waveform models. The two-dimensional contours show the 50% and 90% credible regions, while the vertical lines indicate the 3$\sigma$ intervals of the one-dimensional marginalized posteriors. Results obtained under GR are shown in orange, and those obtained within the varying-$G$ framework are shown in blue.
• Figure 2: Neutron-star sensitivities as a function of mass and gravitational constant for different equations of state. Neutron-star sensitivities are computed for several representative equations of state. The black dashed line shows the empirical relation given in Ref. Lattimer:2010zzZhu:2018etc, while the colored curves correspond to sensitivities obtained from numerical solutions of the TOV equations. The EOSs are taken from Ref. Lattimer:2000nx.
• Figure 3: Workflow for constructing GW waveform templates in a varying-$G$ theory.