<p>Over- and underdensities are simply defined with respect to the mean density <span class="math-container">$\bar{\rho}$</span>.</p>
<p>That is, if <span class="math-container">$\rho(x) &gt; \bar{\rho}$</span>, then <span class="math-container">$\delta(x)$</span> is positive and you call it an overdensity, whereas
if <span class="math-container">$\rho(x) &lt; \bar{\rho}$</span>, then <span class="math-container">$\delta(x)$</span> is negative and you call it an underdensity.</p>
<p>In other words, the threshold you're requesting is <span class="math-container">$\bar{\rho}$</span>.</p>
<p>In cosmology, one is more often interested in the overdensities, because these are the ones that will evolve into the &quot;most interesting&quot; structures, i.e. galaxies, groups, filaments, sheets, and clusters. The underdensities will evolve into voids, which are of course interesting too.</p>
<p>But not as beautiful.</p>

CC BY-SA 4.0
2021-06-22T08:28:47.050Z
Thank you for your nice answer.
Wang Yun
CC BY-SA 4.0
2021-06-22T08:29:47.827Z
@WangYun My pleasure :)
pela
CC BY-SA 4.0
2021-06-22T11:12:08.590Z
The voids *can* be beautiful. If the non void gets too hot it's the perfect place to go...:)
Deschele Schilder
CC BY-SA 4.0
2021-06-22T06:44:05.457Z
2021-06-22T06:44:05.457Z
pela
<p>“Overdense&quot; and &quot;underdense&quot; often appear in various documents to refer to high density and low density respectively. And I know that &quot;overdensity&quot; is defined as</p>
<p><span class="math-container">$$
\delta(x)=\frac{\rho(x)-\bar\rho}{\bar\rho}
$$</span></p>
<p>Is there someone threshold, here denoted as <span class="math-container">$\delta_t$</span> to distinguish &quot;overdense&quot; and &quot;underdense&quot;?</p>

<cosmology><density><matter>
What do "overdense" and "underdense" mean in cosmology?
Wang Yun
# What do "overdense" and "underdense" mean in cosmology?

(Asked by: username_0 on 2021-06-22)

“Overdense" and "underdense" often appear in various documents to refer to high density and low density respectively. And I know that "overdensity" is defined as

$$
\delta(x)=\frac{\rho(x)-\bar\rho}{\bar\rho}
$$

Is there someone threshold, here denoted as $\delta\_t$ to distinguish "overdense" and "underdense"?

**Tags:** cosmology, density, matter


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## 1 answers

### Answer by username_1 on 2021-06-22. Score: 3 | Accepted answer

Over- and underdensities are simply defined with respect to the mean density $\bar{\rho}$.

That is, if $\rho(x) > \bar{\rho}$, then $\delta(x)$ is positive and you call it an overdensity, whereas
if $\rho(x) < \bar{\rho}$, then $\delta(x)$ is negative and you call it an underdensity.

In other words, the threshold you're requesting is $\bar{\rho}$.

In cosmology, one is more often interested in the overdensities, because these are the ones that will evolve into the "most interesting" structures, i.e. galaxies, groups, filaments, sheets, and clusters. The underdensities will evolve into voids, which are of course interesting too.

But not as beautiful.

> **Comments:**
> **username_0**: Thank you for your nice answer.  
> **username_1**: @username_0 My pleasure :)  
> **username_2**: The voids *can* be beautiful. If the non void gets too hot it's the perfect place to go...:)  

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