Simulation Study on Constraining Gravitational Wave Propagation Speed by Gravitational Wave and Gamma-ray Burst Joint Observation on Binary Neutron Star Mergers

Theories of modified gravity suggest that the propagation speed of gravitational waves (GW) vg may deviate from the speed of light c. A constraint can be placed on the difference between c and vg with a simple method that uses the arrival time delay between GW and electromagnetic wave simultaneously emitted from a burst event. We simulated the joint observation of GW and short gamma-ray burst signals from binary neutron star merger events in different observation campaigns, involving advanced LIGO (aLIGO) in design sensitivity and Einstein Telescope (ET) joint-detected with Fermi/GBM. As a result, the relative precision of constraint on vg can reach ∼10−17 (aLIGO) and ∼10−18 (ET), which are one and two orders of magnitude better than that from GW170817, respectively. We continue to obtain the bound of graviton mass mg ≤ 7.1(3.2) × 10−20 eV with aLIGO (ET). Applying the Standard-Model Extension test framework, the constraint on vg allows us to study the Lorentz violation in the nondispersive, nonbirefringent limit of the gravitational sector. We obtain the constraints of the dimensionless isotropic coefficients at mass dimension d = 4, which are for aLIGO and for ET.