<p>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 (<span class="math-container">$z\approx 1090$</span>) and the redshift of the most distant observed galaxy (<span class="math-container">$z\approx 11$</span>), 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.</p>

CC BY-SA 4.0
2021-04-10T06:25:37.960Z
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?
Roger Wood
CC BY-SA 4.0
2021-04-11T14:01:42.880Z
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.
Peter Erwin
CC BY-SA 4.0
2021-04-11T17:37:43.730Z
@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.
Roger Wood
CC BY-SA 4.0
2021-04-11T18:03:18.310Z
@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.
Peter Erwin
CC BY-SA 4.0
2021-04-11T19:47:07.903Z
@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?
Roger Wood
CC BY-SA 4.0
2021-04-10T05:38:08.673Z
2021-04-10T05:38:08.673Z
benrg
<p>This is a follow up to an <a href="https://astronomy.stackexchange.com/questions/43290/is-there-any-correlation-between-the-cosmic-microwave-background-cmb-and-the-">earlier question</a> 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. <br></p>
<p>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 <a href="https://www.sdss.org/" rel="nofollow noreferrer">SDSS</a>.  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).</p>

<galaxy><early-universe><sky-survey><cosmic-microwave-background><infrared>
Are features in the CMB correlated with features in the SDSS map of the most distant galaxies?
Roger Wood
# Are features in the CMB correlated with features in the SDSS map of the most distant galaxies?

(Asked by: username_0 on 2021-04-10)

This is a follow up to an [earlier question](https://astronomy.stackexchange.com/questions/43290/is-there-any-correlation-between-the-cosmic-microwave-background-cmb-and-the-) 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](https://www.sdss.org/). 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).

**Tags:** galaxy, early-universe, sky-survey, cosmic-microwave-background, infrared

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## 1 answers

### Answer by username_1 on 2021-04-10. Score: 3

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.

> **Comments:**
> **username_0**: 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?  
> **username_2**: 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.  
> **username_0**: @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.  
> **username_2**: @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.  
> **username_0**: @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?  

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