  At very high densities, QCD is in the color-flavor locked phase, which is a
color-superconducting phase. The diquark condensates break chiral symmetry in
the same way as it is broken in vacuum QCD and gives rise to an octet of
pseudo-Goldstone bosons and a superfluid mode. The lightest of these are the
charged and neutral kaons. For energies below the superconducting gap, the
kaons are described by an $O(2)\times O(2)$-symmetric effective scalar field
theory with chemical potentials. We use this effective theory to study
Bose-condensation of kaons and their properties as functions of the temperature
and the chemical potentials. We use the 2-particle irreducible effective action
formalism in the Hartree approximation. The renormalization of the gap
equations and the effective potential is studied in detail and we show that the
counterterms are independent of temperature and chemical potentials.We
determine the phase diagram and the medium-dependent quasiparticle masses. It
is shown that the Goldstone theorem is satisfied to a very goodapproximation.
The effects of imposing electric charge neutrality is examined as well.
