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

TL;DR

This paper investigates the conditions under which scalar-tensor theories predict deviations in gravitational wave speed from light speed, and proposes observational strategies to test these deviations using binary systems.

Contribution

It identifies the conditions causing anomalous GW speeds in scalar-tensor theories and suggests using eclipsing binary systems to empirically test for such deviations.

Findings

Conditions for anomalous GW speed involve scalar field breaking Lorentz invariance.

Binary systems like J0651+2844 can test GW speed deviations as small as 2×10⁻¹².

Potential to rule out or confirm models of cosmic acceleration based on GW speed measurements.

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.