New discoveries by LIGO, Virgo and KAGRA are beginning to inform our understanding of dense matter and stellar evolution. The neutron-star/black-hole mergers GW200105 and GW20011 and the heavy neutron-star merger GW190425 have revealed that the gravitational-wave population includes binary systems unlike those previously observed in our Galaxy. We have also used the gravitational-wave data of GW170817 - the first signal from merging neutron stars - to constrain the equation of state of dense matter in neutron stars. With more distant sources typically expected, the distribution of masses in compact binary mergers will become a key observable in the coming years of gravitational-wave astronomy. In this talk, I will discuss methods being used to explore matter and mass properties for LIGO/Virgo neutron stars. I will discuss how these results fit with other neutron-star observations, outline prospects of learning about matter in the current Advanced-detector era, and extrapolate to the potential of next-generation gravitational-wave observatories like Cosmic Explorer to map the phase diagram of dense neutron-rich matter and the endpoints of stellar evolution.
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