Tests of the CMB temperature-redshift relation, CMB spectral distortions and why adiabatic photon production is hard

Abstract

In the expanding Universe, the average temperature of the cosmic microwave background (CMB) is expected to depend like T CMB ∝ (1 + z) on redshift z. Adiabatic photon production (or destruction) or deviations from isotropy and homogeneity could modify this scaling and several observational tests have been carried out in response. Here, we explain why 'adiabatic' conditions are extremely difficult to establish in the redshift range targeted by these tests. Thus, instead of leading to a simple rescaling of the CMB temperature, a spectral distortion should be produced, which can be constrained using COBE/FIRAS. For scenarios with late photon production, tests of the temperature-redshift relation (TRR) should therefore be reinterpreted as weak spectral distortion limits, directly probing the energy dependence of the photon production process. For inhomogeneous cosmologies, an average y-type distortion is produced, but this type of distortion can be created in several other ways. Here, we briefly discuss possible effects that may help disentangling different contributions to the distortion signal, finding this to be very challenging. We furthermore argue that tests of the TRR, using the SZ effect have limited applicability and that for non-gravitational changes to the TRR the CMB anisotropy spectrum should exhibit an additional y-type dependence.

Planck2015 results

“…In practice this approach is consistent with a scaling aT CMB = constant, but with lower precision than obtained here from Planck (e.g., Battistelli et al 2002;Luzzi et al 2009;Saro et al 2014;Hurier et al 2014). A simple T CMB = T 0 (1 + z) 1−β modification to the standard temperature redshift relation is frequently discussed in the literature (though this case is not justified by any physical model and is difficult to realize without creating a CMB spectral distortion, see Chluba 2014). For this parameterization we find β = (0.2 ± 1.4) × 10 −3 Planck TT+lowP+BAO, (84a) β = (0.4 ± 1.1) × 10 −3 Planck TT, TE, EE+lowP+BAO,(84b)…”

“…One is through the energy distribution of the CMB anisotropies (Fixsen et al 1996;Fixsen 2003;Chluba 2014) and another through their power spectra (Opher & Pelinson 2004Chluba 2014 uncertainty in the CMB power spectrum . Overall, the effect of this uncertainty on the parameters of ΛCDM models is small (Hamann & Wong 2008); however, without prior knowledge of T 0 from the COBE/FIRAS measurement, the situation would change significantly.…”

Cosmic microwave background radiation temperature in a dissipative universe

“…[72,73], adiabatic photon production does not affect a blackbody spectrum if radiation fields are not thermalized. Also, Chluba has recently examined the influence of a cosmic microwave background (CMB) spectral distortion and adiabatic photon production processes on the T − z relation in detail [73]. Consequently, it is found that the photon production process does not affect a blackbody spectrum except when the process has a very special energy dependence.…”

“…(For details, see Ref. [73].) Accordingly, if adiabatic photon production for CCDM models [33] is assumed, a weakly dissipative model discussed here should be further constrained because the CMB distortion is neglected in this study.…”

“…Consequently, a weakly dissipative model proposed here is found to be very similar to the standard ΛCDM model because the expected dissipation rate is small. Interestingly, recent works of the radiation temperature [12,13,23,73] imply a more weakly dissipative model. However, the properties of a weakly dissipative model differ from those of a nondissipative ΛCDM model.…”