Fluctuations of the CMB, symmetry between the hot and cold?

[Spinnor]

Consider any of the latest maps of the temperature fluctuations of the CMB. Such a map can be considered a 2 dimensional topographical map of the surface of a sphere, high points hotter, low points cooler. Consider the contours that divide such a map into the two regions, fluctuations hotter then the mean and fluctuations colder then the mean.

If we now take a Fourier transform of only the region hotter then mean and compare that with the Fourier transform of the region cooler then the mean are those Fourier transforms very similar, do they have the same statistics if that question makes sense? Do the temperature fluctuations of the CMB considered as a surface have an inversion symmetry about the mean?

Or put another way, if some graduate student inverted the colors on a fluctuation map would anyone notice, would we still have a plausible fluctuations map (exclude the great void)?

I have taken such a map and with Windows Paint app inverted the colors, seems similar, see attached.

Thanks for any help!

 

[Vanadium 50]

Since these are fluctuations about the average, you can't have an upward fluctuation without a downward fluctuation. Right?

 

[Bill_K]

Do the temperature fluctuations of the CMB considered as a surface have an inversion symmetry about the mean?

Interesting question. I don't think the answer is obvious. There's none apparent to the eyeball, and it would not be revealed in the usual power spectrum. You'd need to look at correlations. I suspect that if there is an asymmetry, at some level the cold fluctuations would be more sharply peaked.