The presence and order of QCD phase transitions from gravitational-wave observations of neutron star mergers

Gravitational-wave observations of neutron star mergers allows us to probe the dense portion of the nuclear equation of state. We develop a formalism for testing the existence and order of phase transitions in the cores of neutron stars using only gravitational-wave observations of their inspiral. We test our formalism on data from the first binary neutron star mergers GW170817 and GW190425, and use synthetic injections assuming the next and uber-next upgrades of the LIGO observatories, A+ and A#, as well as with Cosmic Explorer. We show that populations of mergers in either A+ or A# will be able to measure the existence of a first-order phase transition in observations lasting less than one PhD (less than half a US PhD!). On the other hand, with only the inspiral, we cannot distinguish populations of neutron stars with no phase transition from those with second- or third-order phase transitions or with first-order phase transitions with relatively large transition densities.