Speed of Gravitational Waves and the Fate of Scalar-Tensor Gravity

TL;DR

The paper investigates whether local gravitational-wave propagation can differ from light-speed in scalar-tensor gravity and shows that anomalous propagation requires a nonzero Weyl-coupling arising from Lorentz-violating scalar backgrounds. It derives a Weyl criterion and explicit expressions in Horndeski-type theories, and proposes a phase-lag test using eclipsing binaries observable by LISA to bound $c_g/c-1$ to about $2\times 10^{-12}$ for favorable systems. A null result would dramatically tighten constraints on dark-energy models, while a confirmed anomaly would falsify GR and simple kinetic scalar-tensor theories. The approach, particularly using the white-dwarf binary J0651+2844, provides a practical and powerful means to probe gravity and cosmic acceleration with unprecedented precision.

Abstract

The direct detection of gravitational waves (GWs) is an invaluable new tool to probe gravity and the nature of cosmic acceleration. A large class of scalar-tensor theories predict that GWs propagate with velocity different than the speed of light, a difference that can be $\mathcal{O}(1)$ for many models of dark energy. We determine the conditions behind the anomalous GW speed, namely that the scalar field spontaneously breaks Lorentz invariance and couples to the metric perturbations via the Weyl tensor. If these conditions are realized in nature, the delay between GW and electromagnetic (EM) signals from distant events will run beyond human timescales, making it impossible to measure the speed of GWs using neutron star mergers or other violent events. We present a robust strategy to exclude or confirm an anomalous speed of GWs using eclipsing binary systems, whose EM phase can be exquisitely determined. he white dwarf binary J0651+2844 is a known example of such system that can be used to probe deviations in the GW speed as small as $c_g/c-1\gtrsim 2\cdot 10^{-12}$ when LISA comes online. This test will either eliminate many contender models for cosmic acceleration or wreck a fundamental pillar of general relativity.

Figures (1)

• Figure 1: The phase lag test for the speed of gravity. A compact binary system such as WDS J0651+2844 is monitored both electromagnetically and using GWs. For this geometry (top) only the $+$ GW polarization is emitted in the observer's direction. Its amplitude $h_+$ is initially correlated with the object transverse separation $\Delta x$, but a phase lag (\ref{['eq:phase_lag']}) accumulates on the propagation if $c_g \neq c$ (bottom and right).