Precision constraints on the neutron star equation of state with third-generation gravitational-wave observatories

It is currently unknown how matter behaves at the extreme densities found within the cores of neutron stars. Measurements of the neutron star equation of state probe nuclear physics that is otherwise inaccessible in a laboratory setting. Gravitational waves from binary neutron star mergers encode details about this physics, allowing the equation of state 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 $\gtrsim 3\times 10^5$ 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 $\lesssim 200$ m (90% credibility) in the mass range $1-1.97$ $M_{\odot}$ -- about ten times better than current constraints from LIGO-Virgo-KAGRA and NICER. The constraint is $\lesssim 75$ m (90% credibility) near $1.4-1.6$ $M_{\odot}$ where we assume the the binary neutron star mass distribution is peaked. This constraint is driven primarily from the loudest $\sim 20$ events.