QCD equations of state and speed of sound in neutron stars

Neutron stars are cosmic laboratories to study dense matter in Quantum Chromodynamics (QCD). The observable mass-radius relations of neutron stars are determined by QCD equations of state, and can reflect the properties of QCD phase transitions. In the last decade there have been historical discoveries in neutron stars, the discoveries of two-solar mass neutron stars and neutron star merger events, which have imposed tight constraints on equations of state. While a number of equations of state are constructed to satisfy these constraints, a theoretical challenge is how to reconcile those constructions with the microphysics expected from the hadron physics and in-medium calculations. In this short article we briefly go over recent observations and discuss their implications for dense QCD matter, referring to QCD constraints in the low and high density limits, QCD-like theories, and lattice QCD results for baryon-baryon interactions.