Projected Constraints on Lorentz-Violating Gravity with Gravitational Waves

TL;DR

This paper investigates how gravitational wave observations from neutron star binaries can constrain Lorentz-violating theories of gravity, showing that coincident electromagnetic signals significantly improve the bounds on such violations.

Contribution

It models gravitational wave signals in Lorentz-violating theories using post-Newtonian approximation and demonstrates the potential for future observations to set stringent constraints.

Findings

Third-generation and space-based detectors can provide competitive constraints without electromagnetic counterparts.

A single electromagnetic counterpart can improve bounds by 10 orders of magnitude over current limits.

Constraints are based on differences in gravitational wave group velocity and light speed, detectable via coincident observations.

Abstract

Gravitational waves are excellent tools to probe the foundations of General Relativity in the strongly dynamical and non-linear regime. One such foundation is Lorentz symmetry, which can be broken in the gravitational sector by the existence of a preferred time direction, and thus, a preferred frame at each spacetime point. This leads to a modification in the orbital decay rate of binary systems, and also in the generation and chirping of their associated gravitational waves. We here study whether waves emitted in the late, quasi-circular inspiral of non-spinning, neutron star binaries can place competitive constraints on two proxies of gravitational Lorentz-violation: Einstein-\AE{}ther theory and khronometric gravity. We model the waves in the small-coupling (or decoupling) limit and in the post-Newtonian approximation, by perturbatively solving the field equations in small deformations from General Relativity and in the small-velocity/weak-gravity approximation. We assume a gravitational wave consistent with General Relativity has been detected with second- and third-generation, ground-based detectors, and with the proposed space-based mission, DECIGO, with and without coincident electromagnetic counterparts. Without a counterpart, a detection consistent with General Relativity of neutron star binaries can only place competitive constraints on gravitational Lorentz violation when using future, third-generation or space-based instruments. On the other hand, a single counterpart is enough to place constraints that are 10 orders of magnitude more stringent than current binary pulsar bounds, even when using second-generation detectors. This is because Lorentz violation forces the group velocity of gravitational waves to be different from that of light, and this difference can be very accurately constrained with coincident observations.