Neutron stars host the densest stable matter in the universe. Accurately modeling their multi-messenger astrophysics relies on a detailed description of the equation of state above nuclear density. Astronomical observations of neutron stars can in turn be used to constrain the properties of this dense matter.
On August 17, 2017 the Advanced LIGO and Advanced Virgo detectors discovered the first gravitational-wave signal consistent with a binary neutron star inspiral. The three-dimensional localization of the source using LIGO and Virgo data enabled a successful electromagnetic follow-up campaign that identified an associated kilonova in a galaxy ~40 Mpc from Earth. We are also able to constrain the equation of state of dense matter in neutron stars using the observed gravitational waves. I will outline how these constraints are made, how they connect with other astronomical observations, and outline future prospects for connecting gravitational-wave astronomy with above-nuclear-density physics.