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Gravitational waves observation with electromagnetic counterparts provides anapproach to measure the Hubble constant which is also known as the bright sirenmethod. Great hope has been put into this method to arbitrate the Hubbletension. In this study, we apply the simulation tool \GWT\, and modeling of theaLIGO-design background to simulate the bright siren catalogues ofsub-threshold double neutron star mergers with potential contamination fromnoise and dis-pairing between gravitational waves and electromagneticcounterparts. The Hubble constant and other cosmology parameters are thusinferred from the simulated catalogues with a Bayesian method. From oursimulation study, we reach the following conclusions: 1) the measurement errorof the $H_0$ decreases with a lower signal-to-noise ratio threshold (orequivalently the $P_{\rm astro}$) in the region where $P_{\rm astro} \gtrsim $0.1, while the inferred most probable $H_0$ trends to bias towards largervalues; and 2) other higher order cosmological parameters such as $\Omega_{m}$remain unconstrained even with the sub-threshold catalogues. We also discussadding the network of the gravitational wave detectors to the simulation tooland the electromagnetic counterparts follow-up efficiency simulation, whichwill improve our work in the future.

A simulation study on the constraints of the Hubble constant using sub-threshold GW observation on double neutron star mergers