  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 not available.
Gravitational wave (GW) signals from compact object binaries provide a direct
measurement of their luminosity distances, but not their redshifts. Unlike in
the past, here we employ a realistic EoS parametrization 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 uncertainties in the EoS and the mass parameters estimated from GW data.
Combining the inferred BNS redshifts with the corresponding luminosity
distances, one constructs a redshift-distance relation 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 $\lesssim 5\%$ (with a $90\%$
credible interval) with a realistic distribution of a thousand BNSs, while
allowing for uncertainties in their EoS parameters. Such a measurement can
potentially resolve the current tension in the measurements of the Hubble
constant from the early- and late-time universe. The methodology implemented in
this work demonstrates a comprehensive prescription for inferring the NS EoS
and the Hubble constant by simultaneously combining GW observations from
merging NSs, while employing a simple population model for NS masses and
keeping the merger rate of NSs constant in redshift. This method can be
immediately extended to incorporate merger rate, population properties, and
additional cosmological parameters.
