I am curious about how a particle's kinetic energy changes with the explansion of the unverse. I calculated that for a matter dominated universe it would vary as 1/a2, while the photon temperature varies as 1/a. Is this correct? Is this also true in general? If so, the implication would be that assuming equlibrium at the time of recombination, the temperature of the atomic hydrogen gas that dominates bryonic matter would about 0.003 oK. Would this be detectible by finding very narrow fraunhoffer lines of light passing through this gas?