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This is a follow up to an earlier question to which @pela gave an excellent answer. Apparently the statistics of the length-scales of the CMB fluctuations are similar to those obtained from other measurements.

This question is more specific in asking whether any of the structures observed in the CMB are also observed in the distribution of the most ancient galaxies such as from the Sloan Sky Survey SDSS. So this is specifically asking whether there is a significant positive cross-correlation between between the different measurements (rather than whether their autocorrelations are similar).

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There shouldn't be any correlation. The CMB light that we see is from a spherical region in the early universe. Its homogeneity strongly suggests that the interior of the sphere was just as homogeneous, but we can't actually see CMB light from the interior. The galaxies that we can see formed from matter inside the sphere, and quite far from the edge. Between the CMB redshift ($z\approx 1090$) and the redshift of the most distant observed galaxy ($z\approx 11$), light traveled a comoving distance of roughly 14 Gly, around 30% of the radius of the sphere. Therefore only the very largest features of the CMB should be reflected in the distribution of observable galaxies.

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    $\begingroup$ That's a very good point. So, do we know if the very largest features of the CMB are reflected in the distribution of observable galaxies? $\endgroup$
    – Roger Wood
    Commented Apr 10, 2021 at 6:25
  • $\begingroup$ The key point is that the CMB light and the light from the (relatively) nearby galaxies in SDSS are from completely different and causally unrelated parts of the universe. $\endgroup$
    – Peter Erwin
    Commented Apr 11, 2021 at 14:01
  • $\begingroup$ @Peter Erwin Distant galaxies are necessarily within the light-cone of the CMB that we can see behind them, and can thus be causally related. If the 30% radius (between z=11 and 1090) is correct, then we might expect some correlation between the CMB and structures subtending more than about 30 degrees in the sky. $\endgroup$
    – Roger Wood
    Commented Apr 11, 2021 at 17:37
  • $\begingroup$ @RogerWood I think that only works in the sense that CMB light from the recombination passed through the location of SDSS galaxies on its way to us, yes. But suggesting that the incipient overdensities visible at $z = 1090$ are in any meaningful way causally related to the (relatively) nearby structure at $z < 1$ doesn't make sense. $\endgroup$
    – Peter Erwin
    Commented Apr 11, 2021 at 18:03
  • $\begingroup$ @PeterErwin Assuming the statistics of the structures are homogeneous and isotropic, then something that subtends 30 degrees in the sky will also span about 30% of the distance to the CMB. Is it correct that the distance to z=11 is 70% of the distance to z = 1060? $\endgroup$
    – Roger Wood
    Commented Apr 11, 2021 at 19:47

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