<h3>CMB fluctuations</h3>
<p>The CMB fluctuations are often analyzed through their <em>power spectrum</em> <span class="math-container">$P(k)$</span>, which is a measure of the extent to which it is &quot;clumpy&quot; on a given scale <span class="math-container">$\ell$</span>, with corresponding wavenumber <span class="math-container">$k = 2\pi/\ell$</span>. The origin of this power spectrum is laid in the very early early Universe, just after the Big Bang, and it is of utmost importance in cosmology, as it specifies how structure subsequently evolves.</p>
<p>Various observations help us constrain <span class="math-container">$P(k)$</span>. For the early Universe, we use the CMB, while at later epochs, the large scale structure of galaxies and, even later, galaxy clusters are helpful. Moreover, absorption lines in the spectra of background quasars enable us to map out the structure via the so-called Lyman <span class="math-container">$\alpha$</span> forest.</p>
<p>The figure below (from <a href="https://ui.adsabs.harvard.edu/abs/2010arXiv1005.1100N" rel="nofollow noreferrer">Norman 2008</a>) show how a single cosmological model (from <a href="https://ui.adsabs.harvard.edu/abs/2004PhRvD..69j3501T" rel="nofollow noreferrer">Tegmark et al. 2004</a>) fit all epochs.</p>
<p><a href="https://i.sstatic.net/bm0XU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bm0XU.png" alt="Pk" /></a></p>
<p>The power spectrum evolves with time, so to compare difference epochs, the figure shows <span class="math-container">$P(k)$</span> for the different observations extrapolated to the current epoch (i.e. today).</p>
<h3>CMB dipole</h3>
<p>Observing the dipole in the CMB is relatively easy because, to within 1 in ~100,000, it is described by the same Planck temperature in all directions. This is not the case for any astrophysical sources, so measuring the dipole in galaxies is less straightforward. With large samples of galaxies it has nevertheless been attempted. For 1.2 million galaxies in the WISE catalogue, <a href="https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.1772R" rel="nofollow noreferrer">Rameez et al. (2018)</a> find the dipole anisotropy to be consistent with that of the CMB.</p>

CC BY-SA 4.0
2021-04-07T19:58:59.300Z
That's a super answer, thank you.  It looks like the spectral-density of fluctuations is preserved over time and follows a particular behavior.  Has there been any work done trying to cross-correlate these measurements?  i.e. are any specific features (other than the dipole anisotropy) that have been preserved over time?
Roger Wood
CC BY-SA 4.0
2021-04-10T00:54:28.410Z
@RogerWood I wonder if that's best asked as a new question that links back here? That way it reaches many more readers and may generate new answers.
uhoh
CC BY-SA 4.0
2021-04-10T02:22:39.913Z
@uhoh let me try :-)
Roger Wood
CC BY-SA 4.0
2021-04-10T13:54:29.733Z
@RogerWood Sorry, didn't see your question until now, but yes, as uhoh says it's a good idea to create a new question. And as the answer says there, the CMB power spectrum and the galaxy power spectrum correlate in a statistical way, but not through specific features, since they correspond to vastly different places in space.
pela
CC BY-SA 4.0
2021-04-07T10:57:00.327Z
2021-04-07T10:57:00.327Z
pela
<p>The Cosmic Microwave Background (CMB) is remarkably isotropic but does exhibit a distinct dipolar Doppler shift and also much smaller but measurable fluctuations in intensity and polarization.  Presumably some of these fluctuations should carry over into the subsequent formation of early galaxies and other structures.  To what extent is this expected and to what extent has this been observed?  <br></p>
<p>The CMB Doppler shift is attributed to our local velocity with respect to the early universe. Is this Doppler-shift equally observed with respect to distant galaxies and diffuse starlight?  <br></p>
<p>More particularly, is any of the fine structure in the CMB represented in the distribution or properties of the most ancient objects that can be observed optically (infrared)?</p>

<galaxy><early-universe><sky-survey><cosmic-microwave-background><infrared>
Is there any correlation between the Cosmic Microwave Background (CMB) and the distribution of distant galaxies?
Roger Wood
# Is there any correlation between the Cosmic Microwave Background (CMB) and the distribution of distant galaxies?

(Asked by: username_0 on 2021-04-06)

The Cosmic Microwave Background (CMB) is remarkably isotropic but does exhibit a distinct dipolar Doppler shift and also much smaller but measurable fluctuations in intensity and polarization. Presumably some of these fluctuations should carry over into the subsequent formation of early galaxies and other structures. To what extent is this expected and to what extent has this been observed?

The CMB Doppler shift is attributed to our local velocity with respect to the early universe. Is this Doppler-shift equally observed with respect to distant galaxies and diffuse starlight?

More particularly, is any of the fine structure in the CMB represented in the distribution or properties of the most ancient objects that can be observed optically (infrared)?

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

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## 1 answers

### Answer by username_1 on 2021-04-07. Score: 3

### CMB fluctuations

The CMB fluctuations are often analyzed through their *power spectrum* $P(k)$, which is a measure of the extent to which it is "clumpy" on a given scale $\ell$, with corresponding wavenumber $k = 2\pi/\ell$. The origin of this power spectrum is laid in the very early early Universe, just after the Big Bang, and it is of utmost importance in cosmology, as it specifies how structure subsequently evolves.

Various observations help us constrain $P(k)$. For the early Universe, we use the CMB, while at later epochs, the large scale structure of galaxies and, even later, galaxy clusters are helpful. Moreover, absorption lines in the spectra of background quasars enable us to map out the structure via the so-called Lyman $\alpha$ forest.

The figure below (from [Norman 2008](https://ui.adsabs.harvard.edu/abs/2010arXiv1005.1100N)) show how a single cosmological model (from [Tegmark et al. 2004](https://ui.adsabs.harvard.edu/abs/2004PhRvD..69j3501T)) fit all epochs.

[![Pk](https://i.sstatic.net/bm0XU.png)](https://i.sstatic.net/bm0XU.png)

The power spectrum evolves with time, so to compare difference epochs, the figure shows $P(k)$ for the different observations extrapolated to the current epoch (i.e. today).

### CMB dipole

Observing the dipole in the CMB is relatively easy because, to within 1 in ~100,000, it is described by the same Planck temperature in all directions. This is not the case for any astrophysical sources, so measuring the dipole in galaxies is less straightforward. With large samples of galaxies it has nevertheless been attempted. For 1.2 million galaxies in the WISE catalogue, [Rameez et al. (2018)](https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.1772R) find the dipole anisotropy to be consistent with that of the CMB.

> **Comments:**
> **username_0**: That's a super answer, thank you.  It looks like the spectral-density of fluctuations is preserved over time and follows a particular behavior.  Has there been any work done trying to cross-correlate these measurements?  i.e. are any specific features (other than the dipole anisotropy) that have been preserved over time?  
> **username_2**: @RogerWood I wonder if that's best asked as a new question that links back here? That way it reaches many more readers and may generate new answers.  
> **username_0**: @uhoh let me try :-)  
> **username_1**: @RogerWood Sorry, didn't see your question until now, but yes, as uhoh says it's a good idea to create a new question. And as the answer says there, the CMB power spectrum and the galaxy power spectrum correlate in a statistical way, but not through specific features, since they correspond to vastly different places in space.  

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