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It is currently unknown how matter behaves at the extreme densities found within the cores of neutron stars. Gravitational waves from binary neutron star mergers encode rich information about the stars' deformability, allowing the equation of state---and hence nuclear physics---to be inferred. Planned third-generation gravitational-wave observatories, having vastly improved sensitivity, are expected to provide tight constraints on the neutron star equation of state. We combine simulated observations of binary neutron star mergers by the third-generation observatories Cosmic Explorer and Einstein Telescope to determine future constraints on the equation of state across a plausible neutron star mass range. In one year of operation, a network consisting of one Cosmic Explorer and the Einstein Telescope is expected to detect 310^5 binary neutron star mergers. By considering only the 75 loudest events, we show that such a network will be able to constrain the neutron star radius to at least 200 m (90% credibility) in the mass range 1--1. 97M_---about ten times better than current constraints from LIGO-Virgo-KAGRA and NICER. The constraint is 75 m (90% credibility) near 1. 4--1. 6M_ where we assume the binary neutron star mass distribution is peaked. This constraint is driven primarily from the loudest 20 events.
Walker et al. (2024) studied this question.