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Gravitational-wave measurements of the tidal deformability in neutron-starbinary coalescences can be used to infer the still unknown equation of state(EoS) of dense matter above the nuclear saturation density. By employing aBayesian-ranking test we quantify the ability of current and futuregravitational-wave observations to discriminate among families ofnuclear-physics based EoS which differ in particle content and ab-initiomicroscopic calculations. While the constraining power of GW170817 is limited,we show that even twenty coalescences detected by LIGO-Virgo at designsensitivity are not enough to discriminate between EoS with similar softnessbut distinct microphysics. However, just a single detection with athird-generation detector such as the Einstein Telescope or Cosmic Explorerwill rule out several families of EoS with very strong statisticalsignificance, and can discriminate among models which feature similar softness,hence constraining the properties of nuclear matter to unprecedented levels.

Ranking Love numbers for the neutron star equation of state: The need for third-generation detectors