  At asymptotic high density and low temperature quarks form Cooper pairs in a
color-flavor locked (CFL) configuration. The diquark condensates break
spontaneously the baryon symmetry, and this fact makes the CFL phase also
superfluid. At low temperatures the transport properties are dominated by the
contribution of the superfluid phonon, the Goldstone boson associated to baryon
symmetry breaking, in full analogy to what happens in superfluid He4. We
discuss how to derive transport properties in the ultracold regime making use
of an analogue model of gravity. We also review how this model can be used to
study the scattering of phonons with quantized vortices in a rotating system.
Finally, we consider the implications of these results in studying the
rotational properties of compact stars made of CFL quark matter
