<p><strong>tl;dr nothing is oscillating now, but it was in the early universe. Now we just see the frozen relics</strong></p>
<p>This is just an attempt at a simplified explanation of the Wikipedia article linked in the question.</p>
<p>There were pressure waves in the very early universe. They came from a balance of gravity and radiation pressure (the matter at the time was hot enough to be opaque). Whereever there happened to be a locally higher density (of matter, radiation and dark matter) the excess pressure would cause an expansion and then gravity would cause a contraction sending waves out at (according to the article) half the speed of light.</p>
<p>As the universe expanded and cooled, matter eventually became transparent (it was hydrogen and helium gas) letting the radiation pressure escape and leaving higher densities both in the location of the original concentration and at the crest of the wave a certain distance away (but the same certain distance for the first waves from each concentration). Those high densities are where the galaxies formed, so what we look for today is an excess of galaxies at a specific separation and that's what we see.</p>

CC BY-SA 4.0
2020-07-23T03:44:18.747Z
Okay this is helpful thank you! In hot opaque matter is radiation pressure sufficient for pressure waves to exist and gravity just modifies the waves' behavior, or do you need both for the waves to exits?
uhoh
CC BY-SA 4.0
2020-07-23T09:19:05.643Z
@uhoh My understanding is that gravity was important (but I'm no expert). Since dark matter is affected by gravity but *not* by radiation pressure, the behaviour of the waves depends on the ratio of dark matter to baryonic matter. Observations are consistent with the ratio determined in other ways which is one of the reasons for Dark Matter being broadly accepted as real.
Steve Linton
CC BY-SA 4.0
2020-07-23T11:48:28.120Z
That's really helpful, thank you! If you think it can, maybe consider incorporating that into the answer post itself?
uhoh
CC BY-SA 4.0
2020-07-23T15:24:17.090Z
@uhoh I'll need to look for a source.
Steve Linton
CC BY-SA 4.0
2020-08-02T08:49:01.483Z
I just saw [An Alternative to Dark Matter Passes Critical Test](https://www.quantamagazine.org/modified-gravity-theory-passes-a-critical-test-20200728/) and found it quite interesting and the explanations understandable, including the discussion on "one of the reasons for Dark Matter being broadly accepted as real". It links to several recent papers in arXiv.
uhoh
CC BY-SA 4.0
2021-08-08T10:39:32.103Z
"Whereever there happened to be a locally higher density (of matter, radiation and dark matter) the excess pressure would cause an expansion and then gravity would cause a contraction" -- this kind of has it backwards. A locally higher (DM) density induces gravitational contraction, which increases the baryon density and thus its pressure, which *then* causes expansion.
Peter Erwin
CC BY-SA 4.0
2020-07-22T19:21:22.790Z
2020-07-22T19:21:22.790Z
Steve Linton
<p><strong>Jeans instability theory</strong></p>
<p>Consider a spherical cloud of gas with density <span class="math-container">$\rho$</span> and radius <span class="math-container">$R$</span>. If there were no pressure, the sphere would collapse in the time scale of the free fall time
<span class="math-container">$$t_{ff} = \sqrt{\frac{3\pi}{32G\rho}}$$</span></p>
<p>If there is pressure instead, when the cloud starts to compress, pressure will try to oppose gravity and restore the previous size of the cloud. But pressure doesn't act instantaneously, pressure changes propagate at the speed of sound <span class="math-container">$c_s$</span>. The time it takes for the pressure to react is therefore</p>
<p><span class="math-container">$$t_p = \frac{R}{c_s}$$</span></p>
<p>If <span class="math-container">$t_p \gg t_{ff}$</span> the pressure is not fast enough and the cloud collapses, increasing its density. If <span class="math-container">$t_p \ll t_{ff}$</span> the pressure reacts and the cloud starts damped oscillations.</p>
<p>It is useful to define the Jeans length <span class="math-container">$\lambda_J$</span> or <span class="math-container">$R_J$</span> that is the maximum size a given cloud can have before being doomed to collapse and is found by equating <span class="math-container">$t_p$</span> and <span class="math-container">$t_{ff}$</span>.</p>
<p><span class="math-container">$$\lambda_J \approx {c_s \over \sqrt{G\rho}}$$</span></p>
<p><strong>Different components of the universe</strong></p>
<p>In the early universe the main components to the total matter-energy density where:</p>
<ul>
<li><p>Dark Matter: has no pressure, therefore <span class="math-container">$\lambda_J$</span> is zero. Every clump of dark matter inevitably collapses under gravity, forming dark matter overdensities and gravitational wells.</p>
</li>
<li><p>Radiation: a gas made of photons and relativistic particles has a sound speed that is comparable with the speed of light <span class="math-container">$c_s \approx c$</span>. <span class="math-container">$\lambda_J$</span> is very big, comparable with the size of the causal horizon of the universe. As a consequence, a relativistic gas never collapses under gravity.</p>
</li>
<li><p>Baryonic Matter: before z=1100 photons and electrons where tightly coupled. There were a lot more photons than baryons. The universe was a relativistic soup with <span class="math-container">$c_s \approx c$</span>.
After z=1100 matter and radiation decouple, and <span class="math-container">$c_s$</span> becomes much smaller, the jeans length being about the size of a small galaxy.</p>
</li>
</ul>
<p><strong>A brief history of the formation of structures in the universe</strong></p>
<p>The initial density fluctuations were given (possibly?) by inflation. After inflation, dark matter started collapsing, forming gravitational wells, which later will be fundamental for the formation of galaxies. Baryonic matter instead is coupled with radiation and can only oscillate with very fast and large sound waves.</p>
<p>We know that there is much more dark matter than baryonic matter, but the baryonic oscillations can have a small gravitational effect on dark matter nonetheless. The baryonic oscillations leave a small imprint on the distribution of dark matter. Dark matter oscillates a little bit too.</p>
<p>After the age of decoupling (z=1100) the oscillations freeze. The barions are free to start forming structures and galaxies, but there is so little time! It can be shown that if there were only baryons, the density fluctuation could grow only by a factor of <span class="math-container">$\approx 1000$</span> from the age of decoupling to today. This isn't enough to explain the extreme density differences we observe today: a galaxy is much more dense than the surrounding space.</p>
<p>Luckily there is dark matter, which has already formed the convenient potential wells. Baryonic matter just needs to fall into the wells and form galaxies, stars, planets...</p>
<p>But dark matter had felt the oscillations of the baryons, therefore the spatial distribution of potential wells must carry information of these oscillations. This means that if we look at the spatial distribution of galaxies today, we might be able to see that galaxies like to aggregate more on some spatial scales than in others.</p>
<p><strong>Observation of BAO (baryonic acoustic oscillations)</strong></p>
<p>In particular, we may want to look at the two point correlation function of the spatial distribution of galaxies <span class="math-container">$\xi(r,r')$</span>. Given that there is a galaxy at the position <span class="math-container">$r$</span>, <span class="math-container">$\xi(r,r')$</span> gives the probability that you will find another galaxy at the position <span class="math-container">$r'$</span>. The Fourier transform of <span class="math-container">$\xi$</span> gives the power spectral density <span class="math-container">$P(k)$</span>. It can be calculated theoretically. Using our best fit cosmological parameters <span class="math-container">$P(k)$</span> is the following</p>
<p><a href="https://i.sstatic.net/qVbHS.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qVbHS.png" alt="power spectral density" /></a></p>
<p>Notice the small wiggles to the right of the peak. Those are the imprint of the BAO on the distribution of dark matter, that eventually gives the distribution of galaxies.</p>
<p>This plot is obtained from <a href="https://lambda.gsfc.nasa.gov/toolbox/tb_camb_form.cfm" rel="nofollow noreferrer">CAMB web interface</a>, a website were you can choose the cosmological parameters and after a few seconds it calculates the power spectral density, along with the CMB spectrum and other cosmological observables.</p>
<p>The plank satellite has measured the power spectral density and this is the result.</p>
<p><a href="https://i.sstatic.net/aoQdJ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/aoQdJ.png" alt="plank measures" /></a></p>
<p>This image was made by &quot;ESA and the Planck Collaboration&quot; (<a href="https://arxiv.org/pdf/1807.06205.pdf" rel="nofollow noreferrer">arXiv:1807.06205</a>)</p>

CC BY-SA 4.0
2021-08-08T09:44:12.667Z
2021-08-08T09:44:12.667Z
Prallax
<p>Sci-News' <a href="http://www.sci-news.com/astronomy/eboss-map-universe-08656.html" rel="nofollow noreferrer">Sloan Digital Sky Survey Collaboration Releases New 3D Map of Universe</a> links to the two videos</p>
<ul>
<li><a href="https://youtu.be/KJJXbcf8kxA" rel="nofollow noreferrer">The eBOSS 3D map of the Universe</a></li>
<li><a href="https://youtu.be/TKiYOnsE8Y4" rel="nofollow noreferrer">SDSS releases largest 3D map of the universe ever created</a></li>
</ul>
<p>and says</p>
<blockquote>
<p>The team’s results will be published in a series of 20 papers in the Monthly Notices of the Royal Astronomical Society.</p>
</blockquote>
<p>After <code>01:30</code> in the second video Jiamin Hou from the Max Planck Institute for Extraterrestrial Physics says:</p>
<blockquote>
<p>However the red shift has an additional component that is due to the galaxy’s own velocity, and which moves in response to the gravitational attraction of the surrounding matter, and these two components can not be separated from each other. But the statistical analysis of the eBOSS allows us to distinguish the effects of velocity from that of expansion.</p>
</blockquote>
<p>I've also looked at:</p>
<ul>
<li>Wikipedia: <a href="https://en.wikipedia.org/wiki/Baryon_acoustic_oscillations#Cosmic_sound" rel="nofollow noreferrer">Baryon_acoustic_oscillations; Cosmic sound</a></li>
<li>SDSS.org's <a href="https://www.sdss.org/surveys/eboss/" rel="nofollow noreferrer">surveys; eBOSS</a></li>
</ul>
<p>but I can't get a grasp of what the term &quot;baryon acoustic oscillations&quot; really means.</p>
<p><strong>Question:</strong> Is it possible to <em>write or quote a basic explanation</em> of what these are? For example, does oscillation mean there are things moving back and forth due to some restoring force? Is there something analogous to a &quot;sound wave&quot; out there somewhere? Or is there just a plot of something that shows a wiggly line that goes up and down?</p>

CC BY-SA 4.0
2020-07-22T17:15:07.660Z
are there other tags that should be included?
uhoh
<observational-astronomy><cosmology><sky-survey><sound>
Basic explanation of baryon acoustic oscillations; what if anything is actually oscillating?
uhoh
# Basic explanation of baryon acoustic oscillations; what if anything is actually oscillating?

(Asked by: username_0 on 2020-07-22)

Sci-News' [Sloan Digital Sky Survey Collaboration Releases New 3D Map of Universe](http://www.sci-news.com/astronomy/eboss-map-universe-08656.html) links to the two videos

* [The eBOSS 3D map of the Universe](https://youtu.be/KJJXbcf8kxA)
* [SDSS releases largest 3D map of the universe ever created](https://youtu.be/TKiYOnsE8Y4)

and says

> The team’s results will be published in a series of 20 papers in the Monthly Notices of the Royal Astronomical Society.

After `01:30` in the second video Jiamin Hou from the Max Planck Institute for Extraterrestrial Physics says:

> However the red shift has an additional component that is due to the galaxy’s own velocity, and which moves in response to the gravitational attraction of the surrounding matter, and these two components can not be separated from each other. But the statistical analysis of the eBOSS allows us to distinguish the effects of velocity from that of expansion.

I've also looked at:

* Wikipedia: [Baryon\_acoustic\_oscillations; Cosmic sound](https://en.wikipedia.org/wiki/Baryon_acoustic_oscillations#Cosmic_sound)
* SDSS.org's [surveys; eBOSS](https://www.sdss.org/surveys/eboss/)

but I can't get a grasp of what the term "baryon acoustic oscillations" really means.

**Question:** Is it possible to *write or quote a basic explanation* of what these are? For example, does oscillation mean there are things moving back and forth due to some restoring force? Is there something analogous to a "sound wave" out there somewhere? Or is there just a plot of something that shows a wiggly line that goes up and down?

**Tags:** observational-astronomy, cosmology, sky-survey, sound
> **Comments:**
> **username_0**: are there other tags that should be included?  

---

## 2 answers

### Answer by username_1 on 2020-07-22. Score: 2

**tl;dr nothing is oscillating now, but it was in the early universe. Now we just see the frozen relics**

This is just an attempt at a simplified explanation of the Wikipedia article linked in the question.

There were pressure waves in the very early universe. They came from a balance of gravity and radiation pressure (the matter at the time was hot enough to be opaque). Whereever there happened to be a locally higher density (of matter, radiation and dark matter) the excess pressure would cause an expansion and then gravity would cause a contraction sending waves out at (according to the article) half the speed of light.

As the universe expanded and cooled, matter eventually became transparent (it was hydrogen and helium gas) letting the radiation pressure escape and leaving higher densities both in the location of the original concentration and at the crest of the wave a certain distance away (but the same certain distance for the first waves from each concentration). Those high densities are where the galaxies formed, so what we look for today is an excess of galaxies at a specific separation and that's what we see.

> **Comments:**
> **username_0**: Okay this is helpful thank you! In hot opaque matter is radiation pressure sufficient for pressure waves to exist and gravity just modifies the waves' behavior, or do you need both for the waves to exits?  
> **username_1**: @uhoh My understanding is that gravity was important (but I'm no expert). Since dark matter is affected by gravity but *not* by radiation pressure, the behaviour of the waves depends on the ratio of dark matter to baryonic matter. Observations are consistent with the ratio determined in other ways which is one of the reasons for Dark Matter being broadly accepted as real.  
> **username_0**: That's really helpful, thank you! If you think it can, maybe consider incorporating that into the answer post itself?  
> **username_1**: @uhoh I'll need to look for a source.  
> **username_0**: I just saw [An Alternative to Dark Matter Passes Critical Test](https://www.quantamagazine.org/modified-gravity-theory-passes-a-critical-test-20200728/) and found it quite interesting and the explanations understandable, including the discussion on "one of the reasons for Dark Matter being broadly accepted as real". It links to several recent papers in arXiv.  
> **username_2**: "Whereever there happened to be a locally higher density (of matter, radiation and dark matter) the excess pressure would cause an expansion and then gravity would cause a contraction" -- this kind of has it backwards. A locally higher (DM) density induces gravitational contraction, which increases the baryon density and thus its pressure, which *then* causes expansion.  

---

### Answer by username_3 on 2021-08-08. Score: 2

**Jeans instability theory**

Consider a spherical cloud of gas with density $\rho$ and radius $R$. If there were no pressure, the sphere would collapse in the time scale of the free fall time
$$t\_{ff} = \sqrt{\frac{3\pi}{32G\rho}}$$

If there is pressure instead, when the cloud starts to compress, pressure will try to oppose gravity and restore the previous size of the cloud. But pressure doesn't act instantaneously, pressure changes propagate at the speed of sound $c\_s$. The time it takes for the pressure to react is therefore

$$t\_p = \frac{R}{c\_s}$$

If $t\_p \gg t\_{ff}$ the pressure is not fast enough and the cloud collapses, increasing its density. If $t\_p \ll t\_{ff}$ the pressure reacts and the cloud starts damped oscillations.

It is useful to define the Jeans length $\lambda\_J$ or $R\_J$ that is the maximum size a given cloud can have before being doomed to collapse and is found by equating $t\_p$ and $t\_{ff}$.

$$\lambda\_J \approx {c\_s \over \sqrt{G\rho}}$$

**Different components of the universe**

In the early universe the main components to the total matter-energy density where:

* Dark Matter: has no pressure, therefore $\lambda\_J$ is zero. Every clump of dark matter inevitably collapses under gravity, forming dark matter overdensities and gravitational wells.
* Radiation: a gas made of photons and relativistic particles has a sound speed that is comparable with the speed of light $c\_s \approx c$. $\lambda\_J$ is very big, comparable with the size of the causal horizon of the universe. As a consequence, a relativistic gas never collapses under gravity.
* Baryonic Matter: before z=1100 photons and electrons where tightly coupled. There were a lot more photons than baryons. The universe was a relativistic soup with $c\_s \approx c$.
  After z=1100 matter and radiation decouple, and $c\_s$ becomes much smaller, the jeans length being about the size of a small galaxy.

**A brief history of the formation of structures in the universe**

The initial density fluctuations were given (possibly?) by inflation. After inflation, dark matter started collapsing, forming gravitational wells, which later will be fundamental for the formation of galaxies. Baryonic matter instead is coupled with radiation and can only oscillate with very fast and large sound waves.

We know that there is much more dark matter than baryonic matter, but the baryonic oscillations can have a small gravitational effect on dark matter nonetheless. The baryonic oscillations leave a small imprint on the distribution of dark matter. Dark matter oscillates a little bit too.

After the age of decoupling (z=1100) the oscillations freeze. The barions are free to start forming structures and galaxies, but there is so little time! It can be shown that if there were only baryons, the density fluctuation could grow only by a factor of $\approx 1000$ from the age of decoupling to today. This isn't enough to explain the extreme density differences we observe today: a galaxy is much more dense than the surrounding space.

Luckily there is dark matter, which has already formed the convenient potential wells. Baryonic matter just needs to fall into the wells and form galaxies, stars, planets...

But dark matter had felt the oscillations of the baryons, therefore the spatial distribution of potential wells must carry information of these oscillations. This means that if we look at the spatial distribution of galaxies today, we might be able to see that galaxies like to aggregate more on some spatial scales than in others.

**Observation of BAO (baryonic acoustic oscillations)**

In particular, we may want to look at the two point correlation function of the spatial distribution of galaxies $\xi(r,r')$. Given that there is a galaxy at the position $r$, $\xi(r,r')$ gives the probability that you will find another galaxy at the position $r'$. The Fourier transform of $\xi$ gives the power spectral density $P(k)$. It can be calculated theoretically. Using our best fit cosmological parameters $P(k)$ is the following

[![power spectral density](https://i.sstatic.net/qVbHS.png)](https://i.sstatic.net/qVbHS.png)

Notice the small wiggles to the right of the peak. Those are the imprint of the BAO on the distribution of dark matter, that eventually gives the distribution of galaxies.

This plot is obtained from [CAMB web interface](https://lambda.gsfc.nasa.gov/toolbox/tb_camb_form.cfm), a website were you can choose the cosmological parameters and after a few seconds it calculates the power spectral density, along with the CMB spectrum and other cosmological observables.

The plank satellite has measured the power spectral density and this is the result.

[![plank measures](https://i.sstatic.net/aoQdJ.png)](https://i.sstatic.net/aoQdJ.png)

This image was made by "ESA and the Planck Collaboration" ([arXiv:1807.06205](https://arxiv.org/pdf/1807.06205.pdf))


---

