Simultaneous inference of neutron star equation of state and the 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 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.

Figure 1

90% credible interval of mass-radius priors are shown corresponding to three different choices of EoS prior distributions, as described in Table 1. The solid black line corresponds to the injected EoS.

Figure 2

Constraint on the EoS parameters and $H_0$ by combining 50 GW events as detected by CE using EoS Prior 1. The black lines show the injected values. The median and $1\sigma$ credible intervals are also shown in the respective marginalized one-dimensional posterior.

Figure 3

Same as in Fig. 2 but now using EoS Prior 2.

Figure 4

Same as in Fig. 2 but now using EoS Prior 3.

Figure 5

90% credible interval of mass-radius posteriors are shown using three different choices of the EoS prior distributions as mentioned in Table 1. The solid black curve in each plot is the mass-radius plot corresponding to the injected EoS parameters.

Figure 6

Comparison of joint estimate of the Hubble constant over 50 GW events for the different choices of EoS. The black vertical line denotes the injected value of $H_0=70\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. The dashed vertical lines of the same color indicates 90% highest density credible interval corresponding to the histogram of that color.

Figure 7

Comparison of uncertainty in the measurement of $z$, $d_L$, and $H_0$ using a single BNS observation with source-frame mass pair $(1.4+1.26)M_{\odot }$ at different representative distances. Top panel: fractional uncertainty (left vertical axis) and uncertainty (right vertical axis) in the redshift measurement for three choices of EoS prior. Middle panel: fractional uncertainty (left vertical axis) and uncertainty (right vertical axis) in estimating luminosity distance from GW data. Bottom panel: fractional uncertainty of the Hubble constant for different EoS priors considering uniform prior between $10\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and $400\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$.

Figure 8

Inferred joint posterior distributions (90% credible interval) of $R_{\mathrm{skin}}^{48}$ and $R_{\mathrm{skin}}^{208}$ is shown for the different choices of the EoS priors. The black vertical and horizontal lines denote the injected value of the skin thicknesses $R_{\mathrm{skin}}^{208}=0.1873\mathrm{fm}$ and $R_{\mathrm{skin}}^{48}=0.1571\mathrm{fm}$ respectively, corresponding to injected EoS.