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 \textit{Fermi}/GBM. As a result, the relative precision of constraint on $v_g$ can reach $\sim 10^{-17}$ (aLIGO) and $\sim 10^{-18}$ (ET), which are one and two orders of magnitude better than that from GW170817, respectively. We continue to obtain the bound of graviton mass $m_g \leq 7.1(3.2)\times 10^{-20}\,$eV 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 $\bar{s}_{00}^{(4)}$ at mass dimension $d = 4$, which are $-1\times 10^{-15}< \bar{s}_{00}^{(4)}<9\times 10^{-17}$ for aLIGO and $-4\times 10^{-16}< \bar{s}_{00}^{(4)}<8\times 10^{-18}$ for ET.