Constraining Lorentz-violating, modified dispersion relations with gravitational waves

Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational-wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton’s momentum and deteriorate for a steeper scaling.

Figure 1

ET (left) and LISA (right) spectral noise density curves for the classic design (dotted) and the new NGO design (solid).

Figure 2

Bounds on parameter $\zeta$ for different values of $\alpha$, using AdLIGO and $\rho =10$ (left panel), ET and $\rho =50$ (center panel), and NGO and $\rho =100$ (right panel). Vertical lines at $\alpha =(0,2)$ show where the $\zeta$ correction becomes 100% degenerate with other parameters. Each panel contains several curves that show the bound for systems with different masses.

Figure 3

Bounds on ${\lambda }_g$ (left) and ${\lambda }_{\mathbb{A}}$ (right) as a function of $\eta$ for different total masses, Ad. LIGO, $\rho =10$, and $\alpha =3$.