Projected constraints on Lorentz-violating gravity with gravitational waves

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-AEther 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 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.

Phenomenology of theories of gravity without Lorentz invariance: The preferred frame case

“…[78]. Of particular importance are the differences in the wave-form related to the emission of extra polarizations as compared to GR [74,58] (see [79] for forecasts for testing LV with future observations). A proper understanding of the signal emitted in LV theory also requires the understanding of rotating solutions for which some results can be found in [80,81] …”

Signals for Lorentz violation in gravitational waves

“…It is the normalized Stokes vector for the faster eigenmode and depends on the birefringence angles ϑ and ϕ defined in Eq. (15). The negative-frequency strain can be found using h (D) (f ) = h * (D) (−f ), ensuring that the time-domain strain is real.…”

Constraining alternative polarization states of gravitational waves from individual black hole binaries using pulsar timing arrays

“…We assume all modes travel at the speed of light. However, Lorentz-violating and massive gravity allow for superluminal [25][26][27][28][29][30] and subluminal propagation [1,[31][32][33][34] of non-Einsteinian modes, respectively. Superluminal modes decrease the effective luminosity distance to the binary and the pulsar frequency in that respective altpol's response.…”