Cosmic microwave background radiation temperature in a dissipative universe

Abstract

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 Λ 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 model. Using this relation, the radiation temperature in the late Universe is calculated as a function of a dissipation rate ranging fromμ ¼ 0, corresponding to a nondissipative lambda cold dark matter model, toμ ¼ 1, corresponding to a fully dissipative creation of cold dark matter model. The T − z relation forμ ¼ 0 is linear for standard cosmology and is consistent with observations. However, with increasing dissipation rateμ, 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 cold dark matter model, the T − z relation for lowμ matches observations, whereas the T − z relation for highμ 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.

General form of entropy on the horizon of the universe in entropic cosmology

“…Therefore, the entropic-force model with a nonzero h irr ðtÞ term (not only the constant term but also the H term) is inconsistent with the observed growth rate, especially for a low redshift, as we have previously shown [25]. We have also shown that a weakly dissipative model (similar to the ΛCDM model) describes observations of the cosmic microwave background radiation temperature, whereas a strong dissipative model (similar to the CCDM model) does not [27].…”

“…(17). (Although an entropic-force model in a dissipative universe has been proposed recently, the exchange of energy is neglected [26,27]. More general thermodynamics for matter creation have been discussed by Harko [47].)…”

“…For this purpose, a homogeneous, isotropic, and spatially flat universe is considered, and the scale factor aðtÞ is examined at time t in the FriedmannLemaître-Robertson-Walker metric [23][24][25][26][27]. First, ΛCDM models are briefly reviewed in Sec.…”

“…Moreover, irreversible entropy due to matter creation [26,27] is included in that formulation. Using the present model, we examine whether the entropy on the horizon behaves exchangeably or not.…”

“…As a possible alternative scenario, entropic-force models based on the holographic principle [16], in which several forms of entropy on the horizon of the universe are assumed [17][18][19][20][21][22][23][24][25][26][27][28][29][30], have been recently proposed. For example, the Bekenstein entropy (an area entropy based on additive statistics) [31], the Tsallis-Cirto entropy (a volume entropy based on nonadditive statistics) [32], and a quartic entropy [24,25] have been suggested for the entropy on the horizon [17,25].…”