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Somehow, I have never read about this or thought about, until now...

Does the number of photons from the CMB hitting us from all directions vary at all?

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    $\begingroup$ "The detailed analysis of CMBR data to produce maps, an angular power spectrum, and ultimately cosmological parameters is a complicated, computationally difficult problem." en.wikipedia.org/wiki/… $\endgroup$
    – PM 2Ring
    Mar 29 at 3:42

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The cosmic microwave background (CMB) does of course vary with direction, in terms of its amplitude, temperature and polarisation. It is these variations which lead to its diagnostic power in determining the cosmological parameters (e.g. Planck collaboration 2018).

The fluctuations are accenuated in the ubiquitous plots that you see of the microwave sky. For example this image constructed with data from the ESA Planck satellite. The temperature fluctuations in the intrinsic CMB are at the level of about $\pm 0.0005$ K compared to the mean temperature of 2.73 K (i.e. 1 about 2 parts in $10^5$) so are exaggerated in such plots. The amplitude variations (as a percentage) are a few times bigger. These anisotropies are caused by variation in the plasma conditions at the time of recombination.

enter image description here

The polarisation of the CMB is weak but also varies with position. This is also caused by anisotropies in the plasma at the time of recombination. The equivalent differences in signal level in the polarised light equate to micro-Kelvins in the CMB temperature (i.e. about 100 times weaker than the main temperature variations). The plot below, also taken from ESA's Planck mission, attempts to visualise the polarisation pattern superimposed on a slightly smoothed version of the temperature fluctuation map. The lines/contours show the polarisation direction.

enter image description here

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