The diffuse neutrino and the stochastic gravitational wave (GW) backgrounds from binary neutron star mergers offer a wealth of physics information worth exploring. We study the feasibility of detection of both backgrounds as standalone and as multimessenger observations. Furthermore, we explore the possibility of setting additional constraints to the nuclear matter equation of state (EOS) based on these detections. We find that within the reach of the next generation of GW detectors, this stochastic GW background will show signatures of the EOS, in a frequency range of about 200–300 Hz (subjected to merger rates). As discussed elsewhere, while the detection of these relic neutrinos up to some cosmological distance is challenging, due to the presence of backgrounds from other sources, it is feasible by implementing searches following up the mergers’ GW observation. We find that analyzing the neutrino counts, in Hyper-Kamiokande enhanced with gadolinium (HK-Gd), during short time windows of a few milliseconds and in coincidence with GWs would provide significant background reduction. Additionally, based on this multimessenger strategy, we find that in a bit less than a decade of mergers’ observation, it would be possible to distinguish in HK-Gd between EOS types with a follow-up time window of about a second.

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• Hydrodynamic models
• Nuclear astrophysics
• Nuclear matter in neutron stars
• Nuclear physics of explosive environments