Abstract
We calculate the neutrino mean free path in color superconducting quark matter, and employ it to study the cooling of matter via neutrino diffusion in the superconducting phase as compared to a free quark phase. The cooling process slows when quark matter undergoes a second order phase transition to a superconducting phase at the critical temperature ${T}_{c}.$ Cooling subsequently accelerates as the temperature decreases below ${T}_{c}.$ This will directly impact the early evolution of a newly born neutron star, should its core contain quark matter. Consequently, there may be observable changes in the early neutrino emission which would provide evidence for superconductivity in hot and dense matter.
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