Simulation Study on Constraining GW Propagation Speed by GW and GRB Joint Observation on Binary Neutron Star Mergers

Theories of modified gravity suggest that the propagation speed of gravitational wave (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 (EM) wave simultaneously emitted from a burst event. We simulated the joint observation of GW and short Gamma-Ray burst (sGRB) signals from Binary Neutron Star (BNS) 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^-20eV with aLIGO (ET). Applying the Standard-Model Extension (SME) 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 s̅_00^(4) at mass dimension d = 4, which are -1× 10^-15< s̅_00^(4)<9× 10^-17 for aLIGO and -4× 10^-16< s̅_00^(4)<8× 10^-18 for ET.