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) v g may deviate from the speed of light c . A constraint can be placed on the difference between c and v g 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 v g 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 m g ≤ 7.1(3.2) × 10 −20 eV with aLIGO (ET). Applying the Standard-Model Extension test framework, the constraint on v g 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 s ¯ 00 ( 4 ) at mass dimension d = 4, which are − 1 × 10 − 15 < s ¯ 00 ( 4 ) < 9 × 10 − 17 for aLIGO and − 4 × 10 − 16 < s ¯ 00 ( 4 ) < 8 × 10 − 18 for ET.