Binary neutron stars in the next-generation era: Multi-messenger detection prospects and constraints on the equation of state, mass distribution, and cosmology

Next-generation gravitational-wave (GW) observatories will provide crucial insights into the nature of neutron star (NS) matter and the cosmological expansion history. We estimate the number of multi-messenger detections from binary neutron stars (BNS) with the Einstein Telescope (ET) and Cosmic Explorer (CE), and project the resulting constraints on the equation of state (EOS), BNS mass distribution, and cosmology via joint hierarchical Bayesian inference. Assuming a local merger rate of 106.6 Gpc-3 yr-1 and considering two different mass functions, a narrow one centred around 1.4 M and a wide one ranging between 1.1--2 M, we find that for ET, our mock follow-up algorithm results in at least about40 and up to about100 successfully identified electromagnetic counterparts per year, depending on the detector layout and mass distribution. In a joint network with CE, the number of multi-messenger detections can range from about 200 to about500. Additionally, several more afterglows from gamma-ray bursts or KNe could be found with dedicated late-time observations. Based on the identified multi-messenger events, we perform an injection campaign to hierarchically constrain the EOS, mass distribution, and cosmology in a fully Bayesian framework. Focussing on ET alone, we show how in an ideal scenario, GW signals, KNe, and host galaxy redshifts can constrain the canonical NS radius R 1.4 within about 0.2 km and the Hubble constant H 0 within about 1 km s-1 Mpc-1, while recovering the essential features of the mass distribution. By comparing inference results that rely solely on GW data and those that incorporate light curve information, we find that while KN light-curve posteriors have a negligible impact on the EOS constraints, they can benefit the inference of cosmological parameters.