TITLE: Detection of Variation of CMB Radiation with Time and Space
QUESTION [0 upvotes]: According to the standard model of cosmology, the CMBR temperature increased as $T(z)=2.7(1+z)$ at higher redshift. Has there been any study to actually probe the variation of the CMBR with redshift, or is it possible to do so?
Also, the CMBR power spectrum is plotted with its angular variation. Is it possible to measure the spatial variation of the CMBR, to ensure that it is also homogeneous, on top of being isotropic?
Any research paper on the observational aspects is also welcome.

REPLY [1 votes]: Yes, there has.
There are two ways (at least) to approach this. One is to look at the Sunyaev-Zel'Dovich effect. This is where Compton scattering of Cosmic Microwave Background (CMB) photons by hot intracluster gas in large galaxy clusters causes small changes in the CMB intensity. The frequency dependence of the effect allows an estimate of the CMB temperature at the redshift of the galaxy cluster. This has been done a number of times (e.g. Luzzi et al. 2009, de Martino et al. 2015;Lopez-Corredoira et al. 2017). The results suggest consistency with the relationship $T = T_0(1+z)$ to about 1-2 percent out to redshifts of 0.8.
An alternative approach is to look at the absorption spectra along sightlines to high redshift quasars. In particular, there are some absorbers, both atomic and molecular, that are photo-excited by the CMB. Careful analysis of the relative strengths of fine-structure components of these absorbers leads to an estimate of the temperature of the exciting CMB radiation field (e.g. Molaro et al. 2002) and this can be done to quite high redshifts of $\sim 3$.
The results are again, prefectly consistent with the expected evolution of the CMB temperature to 1-2 percent (e.g. Noterdaeme et al. 2010; Muller et al. 2013).
Avgoustidis et al. (2015) claim that the combined data from the S-Z effect and from quasar sightlines indicate that the temperature of the CMB varies with redshift as expected to 0.7 percent.
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