An advanced LIGO and Virgo’s third observing run brought another binary neutron star merger (BNS) and the first
neutron-star black hole mergers. While no confirmed kilonovae were identified in conjunction with any of these
events, continued improvements of analyses surrounding GW170817 allow us to project constraints on the Hubble
Constant (H0), the Galactic enrichment from r-process nucleosynthesis, and ultra-dense matter possible from
forthcoming events. Here, we describe the expected constraints based on the latest expected event rates from the
international gravitational-wave network and analyses of GW170817. We show the expected detection rate of gravitational waves and their counterparts, as well as how sensitive potential constraints are to the observed numbers of counterparts. We intend this analysis as support for the community when creating scientifically driven electromagnetic follow-up proposals. During the next observing run O4, we predict an annual detection rate of electromagnetic counterparts from BNS of 0.43 0.260.58-+ (1.97 1.22.68-+ ) for the Zwicky Transient Facility (Rubin
Observatory).

Gravitational wave sources, Gravitational wave astronomy, High energy astrophysics, Hubble constant, Astrophysical black holes, Neutron stars, Gravitational waves, Cosmology