Why is the multipole moment l in the power spectra of the CMB corresponds to the radius (instead of diameter) of the sound wave horizon of the baryon-photon fluid?

It seems to me that it should be the diameter (not radius) of the sound wave horizon that decides how large on average could the "rings" of denser areas expand before the recombination.


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The idea of baryon acoustic oscillations (BAO) is that for each region of excess density, there is a spherical shell around it of much weaker excess density. The BAO feature in the correlation function or power spectrum is associated with the distance between the central density excess and the shell, which is precisely the sound horizon.

In principle, there are also the shell-shell correlations that you are thinking about. However, they are much weaker, since the shell itself is of much lower amplitude than the central region. Also, this signature would be smeared out over a range of scales, because the distance between different points on a shell ranges from 0 up to the diameter.


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