Cosmic microwave background radiation temperature in a dissipative universe

The relationship between the cosmic microwave background radiation temperature and the redshift, i.e., the $T$--$z$ relation, is examined in a phenomenological dissipative model. The model contains two constant terms, as if a nonzero cosmological constant $\Lambda$ and a dissipative process are operative in a homogeneous, isotropic, and spatially flat universe. The $T$--$z$ relation is derived from a general radiative temperature law, as appropriate for describing nonequilibrium states in a creation of cold dark matter (CCDM) model. Using this relation, the radiation temperature in the late universe is calculated as a function of a dissipation rate ranging from $\tilde{\mu} =0$, corresponding to a nondissipative $\Lambda$CDM model, to $\tilde{\mu} =1$, corresponding to a fully dissipative CCDM model. The $T$--$z$ relation for $\tilde{\mu} =0$ is linear for standard cosmology and is consistent with observations. However, with increasing dissipation rate $\tilde{\mu}$, the radiation temperature gradually deviates from a linear law because the effective equation-of-state parameter varies with time. When the background evolution of the universe agrees with a fine-tuned pure $\Lambda$CDM model, the $T$--$z$ relation for low $\tilde{\mu}$ matches observations, whereas the $T$--$z$ relation for high $\tilde{\mu}$ does not. Previous work also found that a weakly dissipative model accords with measurements of a growth rate for clustering related to structure formations. These results imply that low dissipation is likely for the universe. The weakly dissipative model should be further constrained by recent observations.