Dense quark matter in nature

According to quantum chromodynamics (QCD), matter at ultra-high densities will take the form of a color-superconducting quark liquid, in which there is a condensate of Cooper pairs of quarks near the Fermi surface. I present a review of the physics of color superconductivity. I give particular attention to the recently proposed gapless CFL (gCFL) phase, which has unusual properties such as quasiquarks with a near-quadratic dispersion relation, and which may well be the favored phase of quark matter in the density range relevant to compact stars. I also discuss the effects of color superconductivity on the mass-radius relationship of compact stars, showing that one would have to fix the bag constant by other measurements in order to see the effects of color superconductivity. An additional parameter in the quark matter equation of state connected with perturbative corrections allows quark matter to imitate nuclear matter over the relevant density range, so that hybrid stars can show a mass-radius relationship very similar to that of nuclear matter, and their masses can reach 1.9 M-circle dot.