|Abstract : ||Gravitational waves (GWs) from compact binary coalescences (CBC) directly provide luminosity distance measurement but no redshift information. If their redshifts were available by alternative means, such as via electromagnetic counterparts, the Hubble constant could be estimated from the distance-redshift relation. However, while binary neutron star (BNS) mergers are expected to be accompanied by electromagnetic counterparts, like GW170817, a redshift measurement may not always be available. Here, we have extended a past proposal for utilizing prior knowledge of neutron star (NS) equation state (EoS) instead to infer the Hubble constant. Unlike in the past, we employ a realistic EoS parameterization in a Bayesian framework to simultaneously measure the Hubble constant and refine the constraints on EoS parameters.
The phase of the frequency domain GW waveform consists of two components: the standard post-Newtonian (PN) point-particle frequency domain phase and the tidal phase component arising due to the tidal deformation of neutron stars. The PN point-particle piece depends on the redshifted chirp-mass and luminosity distance – in contrast to the tidal phase term, which depends on source-frame component masses.
The degeneracy between mass parameters and the redshift is thus broken with the knowledge of EoS. Since GW observation also provides the luminosity distance, the Hubble constant can therefore be inferred.
We demonstrate the performance of our methodology with a mock GW catalog of sources, simulated for Cosmic Explorer – a proposed third-generation GW detector. We consider three sets of priors over EoS parameters and deduce how precisely the Hubble constant can be measured and the EoS parameters constrained in that era.