Astrophysical observations of neutron stars have been widely used to infer
the properties of the nuclear matter equation of state. Beside being a source
of information on average properties of dense matter, however, the data
provided by electromagnetic and gravitational wave (GW) facilities are reaching
the accuracy needed to constrain, for the first time, nuclear dynamics in dense
matter. In this work we assess the sensitivity of current and future neutron
star observations to directly infer the strength of repulsive three-nucleon
forces, which are key to determine the stiffness of the equation of state.
Using a Bayesian approach we focus on the constraints that can be derived on
three-body interactions from binary neutron star mergers observed by second and
third-generation of gravitational wave interferometers. We consider both single
and multiple observations. For current detectors at design sensitivity the
analysis suggests that only low mass systems, with large signal-to-noise ratios
(SNR), allow to reliably constrain the three-body forces. However, our results
show that a single observation with a third-generation interferometer, such as
the Einstein Telescope or Cosmic Explorer, will constrain the strength of the
repulsive three-body potential with exquisite accuracy, turning
third-generation GW detectors into new laboratories to study the nucleon

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