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 of 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 using joint hierarchical Bayesian inference. Our results rely on specific assumptions for the merger rate, EOS, and mass distribution; we consider two different mass functions, a narrow one centred around 1.4 M⊙ and a wide one ranging from 1.1 to 2 M⊙, and a merger rate with a local value of 107 Gpc−3 yr−1. Under this setup, our mock follow-up algorithm results in between ∼40 and ∼100 short-term electromagnetic counterparts per year for ET, depending on the detector layout and mass distribution. In a joint network with CE, this number ranges from ∼100 to ∼500. Additionally, we project tens to hundreds of late-time afterglow detections from gamma-ray bursts or KNe. Based on the generated multi-messenger events, we perform an injection campaign to hierarchically recover the EOS, mass distribution, and cosmology in a fully Bayesian framework. Focussing on KN events from ET alone, the multi-messenger data from our largest analysed catalogue with 78 events can constrain the canonical NS radius R1.4 to ≲ 0.2 km and the Hubble constant H0 to ≲ 1 km s−1 Mpc−1, at least in absence of systematic modelling offsets. By comparing inference results that are solely based on GW data and those incorporating light-curve information, we find that while the latter has negligible impact on the EOS constraints, it can benefit the inference of cosmological parameters.