Simultaneous Inference of Neutron Star Equation of State and Hubble
  Constant with a Population of Merging Neutron Stars
  We develop a method for implementing a proposal on utilizing knowledge of
neutron star (NS) equation of state (EoS) for inferring the Hubble constant
from a population of binary neutron star (BNS) mergers. This method is useful
in exploiting BNSs as standard sirens when their redshifts are unavailable.
Gravitational wave (GW) signals from compact object binaries provide a direct
measurement of their luminosity distances, but not the redshifts. 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 the
EoS parameters. The uncertainty in the redshift depends on the uncertainty in
EoS and mass parameters estimated from GW data. Combining the inferred BNS
redshifts with the corresponding luminosity distances, one constructs a
redshift-distance relationship and deduces the Hubble constant from it. Here,
we show that in the Cosmic Explorer era, one can measure the Hubble constant to
a precision of $\sim 3\%$ (with a $90\%$ credible interval) with a realistic
distribution of thousand BNSs, while allowing for uncertainties in their EoS
parameters. The methodology implemented in this work demonstrates a
comprehensive algorithm to infer NS EoS and the Hubble constant by
simultaneously combining GW observations from merging NSs, choosing a simple
population model of NS masses and keeping the merger rate of NSs constant. This
method can be immediately extended to incorporate merger rate, population
properties, and different cosmological parameters.
