<h4>The insignificance of dark energy</h4>
<p>Structure in the Universe forms in general in a hierarchical way, with small structures collapsing first, later merging to larger structures. But even the largest structures, galaxy clusters, form moderately early, at redhifts of around <span class="math-container">$z\gtrsim1$</span>, when the Universe was roughly half its current age. But dark energy only starts to dominate the dynamics at <span class="math-container">$z\simeq0.3$</span>, when the Universe was some 10 billion years old, and therefore plays a very small to insignificant role in the <em>formation</em> of both over- and underdensities.</p>
<p>The reason that voids expand faster is thus mostly due their inability to retard the overall expansion. But if they're inside a region which, despite the voids small density, in total is an overdensity, there is only the fate of collapse.</p>
<p>Dark energy does play a role in the <em>evolution</em> of voids, and today they hence expand faster and faster. But voids don't exert a force to their surrounding. Distance simply increase faster inside them than outside.</p>
<h4>Squeezing voids</h4>
<p><a href="https://academic.oup.com/mnras/article/350/2/517/1115675" rel="nofollow noreferrer">Sheth &amp; Van De Weygaert (2004, your reference 1)</a> use the phrase that the voids are &quot;squeezed out of existence&quot;. This picturesque description (which I suspect is Rien Van De Weygaert's addition, not Ravi Sheth's) shouldn't be taken too literally; it's just a way to say that they disappear. If you take a void and expand it more along one direction, there is no &quot;elasticity-like&quot; property that would make it collapse perpendicular to this direction.</p>
<p>Both clouds and voids can in general have an ellipsoidal shape. In fact, this was an important addition by Ravi Sheth and Bepi Tormen to the theory of structure formation
(<a href="https://ui.adsabs.harvard.edu/abs/1999MNRAS.308..119S/abstract" rel="nofollow noreferrer">Sheth &amp; Tormen 1999</a>;
<a href="https://ui.adsabs.harvard.edu/abs/2001MNRAS.323....1S/abstract" rel="nofollow noreferrer">2001</a>;
<a href="https://ui.adsabs.harvard.edu/abs/2002MNRAS.329...61S/abstract" rel="nofollow noreferrer">2002</a>) which had, until then, been dominated by the <a href="https://ui.adsabs.harvard.edu/abs/1974ApJ...187..425P/abstract" rel="nofollow noreferrer">Press-Schechter (1974)</a> formalism.</p>

CC BY-SA 4.0
2024-03-09T03:07:16.747Z
thank you for your answer. However, I still have some questions: So, if the fate of a void inside an overdensity is ultimately collapse, as they expand more than the overdensity the radius of the void will grow more quickly. So, when it collapses, and the matter from the outskirts of the void smashes and collapses, shouldn't that region be hotter than the rest of the overdensity, as it run more distance until collapsing (therefore gaining more kinetic energy from potential energy)? @pela
vengaq
CC BY-SA 4.0
2024-03-09T12:34:43.943Z
also, in this paper (https://arxiv.org/abs/1906.00409), the authors say "Small voids are in fact mostly located near the boundaries of large voids, near the surrounding filaments and walls, and are heavily squeezed by the combined effect of the more prominent expansion of their large neighbour(s) and the gravitational influence of the high-density filaments and walls.". So, does this indicate that the expansion of nearby bigger voids can contribute to the "squeezing" or "cruching" of smaller voids? Doesn't this cause collisions of the matter surrounding smaller voids' outskirts? @pela
vengaq
CC BY-SA 4.0
2024-03-09T15:20:36.283Z
@vengaq Wrt. your first question: You're right that, in an overdensity with a void inside, the particles will gain more kinetic energy because they will, on average, be farther from the center. But if you compare the potential energy of a uniform sphere (3GM²/5R) with that of a thin shell (GM²/2R), you'll see that even if you have all the mass concentrated in a thin shell around the void, the difference will be very small. When the overdensity has virialized, it reaches a (virial) temperature that basically depends only of the total mass of the overdensity.
pela
CC BY-SA 4.0
2024-03-09T15:23:09.033Z
@vengaq Regarding your second question, I don't really know enough about the topic to answer this, I think.
pela
CC BY-SA 4.0
2024-03-12T09:41:39.543Z
"When the overdensity has virialized, it reaches a (virial) temperature that basically depends only of the total mass of the overdensity" is it because is an average temperature (and does not account for local differences in the structure)? @pela
vengaq
CC BY-SA 4.0
2024-03-12T12:50:33.540Z
@vengaq It's because this temperature comes from equating the thermal energy of a particle ($\sim k_\mathrm{B}T$) to its potential energy ($\sim GMm/R$). The exact distribution of the mass then introduces a factor of order unity. So it does account for local structures (via this factor), but it's not a huge factor.
pela
CC BY-SA 4.0
2024-03-06T16:43:16.623Z
2024-03-06T16:43:16.623Z
pela
<p>According to some papers I've found <a href="https://academic.oup.com/mnras/article/350/2/517/1115675" rel="nofollow noreferrer">1</a>, <a href="https://arxiv.org/abs/1501.02120" rel="nofollow noreferrer">2</a> expanding voids can be foun inside clouds of denser materials that can cause them to eventually collapse. I have two questions about this:</p>
<ol>
<li><p>Overdensities generally expand up to a given turnaround radius and then collapse. However, as the elements in the overdensity would have been gravitationally bound since the beginning, the expansion would not actually be driven by dark energy. The void however, would expand faster than the overdensity as the interior would have a very low density, and theoretically would not be gravitationally bound, so the expansion of the void would be driven by dark energy. If this is correct, when the void would collapse because of the surrounding overdensity, would the matter be &quot;pushed&quot; to collapse from a greater distance (as it would have been &quot;moved&quot; by dark energy), therefore gaining more kinetic energy than in the rest of the overdensity?</p>
</li>
<li><p>I have also read that voids can expand as an ellipsoid, so that one of the axis expands faster than the other. Could this also cause a collapse of the void? I mean, is it possible that the void gets squeezed by expansion itself, by the enlargement of one of the axis, ending in a collapse of the stucture?</p>
</li>
</ol>

<astrophysics><gravity><cosmology><general-relativity><galaxy-cluster>
Expanding voids ending being collapsed?
vengaq
# Expanding voids ending being collapsed?

(Asked by: username_0 on 2024-03-06)

According to some papers I've found [1](https://academic.oup.com/mnras/article/350/2/517/1115675), [2](https://arxiv.org/abs/1501.02120) expanding voids can be foun inside clouds of denser materials that can cause them to eventually collapse. I have two questions about this:

1. Overdensities generally expand up to a given turnaround radius and then collapse. However, as the elements in the overdensity would have been gravitationally bound since the beginning, the expansion would not actually be driven by dark energy. The void however, would expand faster than the overdensity as the interior would have a very low density, and theoretically would not be gravitationally bound, so the expansion of the void would be driven by dark energy. If this is correct, when the void would collapse because of the surrounding overdensity, would the matter be "pushed" to collapse from a greater distance (as it would have been "moved" by dark energy), therefore gaining more kinetic energy than in the rest of the overdensity?
2. I have also read that voids can expand as an ellipsoid, so that one of the axis expands faster than the other. Could this also cause a collapse of the void? I mean, is it possible that the void gets squeezed by expansion itself, by the enlargement of one of the axis, ending in a collapse of the stucture?

**Tags:** astrophysics, gravity, cosmology, general-relativity, galaxy-cluster

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## 1 answers

### Answer by username_1 on 2024-03-06. Score: 2

#### The insignificance of dark energy

Structure in the Universe forms in general in a hierarchical way, with small structures collapsing first, later merging to larger structures. But even the largest structures, galaxy clusters, form moderately early, at redhifts of around $z\gtrsim1$, when the Universe was roughly half its current age. But dark energy only starts to dominate the dynamics at $z\simeq0.3$, when the Universe was some 10 billion years old, and therefore plays a very small to insignificant role in the *formation* of both over- and underdensities.

The reason that voids expand faster is thus mostly due their inability to retard the overall expansion. But if they're inside a region which, despite the voids small density, in total is an overdensity, there is only the fate of collapse.

Dark energy does play a role in the *evolution* of voids, and today they hence expand faster and faster. But voids don't exert a force to their surrounding. Distance simply increase faster inside them than outside.

#### Squeezing voids

[Sheth & Van De Weygaert (2004, your reference 1)](https://academic.oup.com/mnras/article/350/2/517/1115675) use the phrase that the voids are "squeezed out of existence". This picturesque description (which I suspect is Rien Van De Weygaert's addition, not Ravi Sheth's) shouldn't be taken too literally; it's just a way to say that they disappear. If you take a void and expand it more along one direction, there is no "elasticity-like" property that would make it collapse perpendicular to this direction.

Both clouds and voids can in general have an ellipsoidal shape. In fact, this was an important addition by Ravi Sheth and Bepi Tormen to the theory of structure formation
([Sheth & Tormen 1999](https://ui.adsabs.harvard.edu/abs/1999MNRAS.308..119S/abstract);
[2001](https://ui.adsabs.harvard.edu/abs/2001MNRAS.323....1S/abstract);
[2002](https://ui.adsabs.harvard.edu/abs/2002MNRAS.329...61S/abstract)) which had, until then, been dominated by the [Press-Schechter (1974)](https://ui.adsabs.harvard.edu/abs/1974ApJ...187..425P/abstract) formalism.

> **Comments:**
> **username_0**: thank you for your answer. However, I still have some questions: So, if the fate of a void inside an overdensity is ultimately collapse, as they expand more than the overdensity the radius of the void will grow more quickly. So, when it collapses, and the matter from the outskirts of the void smashes and collapses, shouldn't that region be hotter than the rest of the overdensity, as it run more distance until collapsing (therefore gaining more kinetic energy from potential energy)? @pela  
> **username_0**: also, in this paper (https://arxiv.org/abs/1906.00409), the authors say "Small voids are in fact mostly located near the boundaries of large voids, near the surrounding filaments and walls, and are heavily squeezed by the combined effect of the more prominent expansion of their large neighbour(s) and the gravitational influence of the high-density filaments and walls.". So, does this indicate that the expansion of nearby bigger voids can contribute to the "squeezing" or "cruching" of smaller voids? Doesn't this cause collisions of the matter surrounding smaller voids' outskirts? @pela  
> **username_1**: @vengaq Wrt. your first question: You're right that, in an overdensity with a void inside, the particles will gain more kinetic energy because they will, on average, be farther from the center. But if you compare the potential energy of a uniform sphere (3GM²/5R) with that of a thin shell (GM²/2R), you'll see that even if you have all the mass concentrated in a thin shell around the void, the difference will be very small. When the overdensity has virialized, it reaches a (virial) temperature that basically depends only of the total mass of the overdensity.  
> **username_1**: @vengaq Regarding your second question, I don't really know enough about the topic to answer this, I think.  
> **username_0**: "When the overdensity has virialized, it reaches a (virial) temperature that basically depends only of the total mass of the overdensity" is it because is an average temperature (and does not account for local differences in the structure)? @pela  
> **username_1**: @vengaq It's because this temperature comes from equating the thermal energy of a particle ($\sim k_\mathrm{B}T$) to its potential energy ($\sim GMm/R$). The exact distribution of the mass then introduces a factor of order unity. So it does account for local structures (via this factor), but it's not a huge factor.  

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