<p>It's actually due to the Angular Diameter distance. I still don't understand the exact mechanism, but I can shed some light on it. The angular diameter distance can be written as</p>
<p><span class="math-container">$$d_A = \frac{\chi}{1+z}$$</span></p>
<p>for <span class="math-container">$$\chi = c\int_0^z \frac{dz}{H(z)}$$</span></p>
<p>In the LCDM model, this becomes</p>
<p><span class="math-container">$$\chi = \frac{c}{H_0}\int_0^z \frac{dz}{\sqrt{\Omega_{m,0}(1+z)^3+\Omega_{\Lambda}}}$$</span></p>
<p>Sadly, it's nearly impossible to integrate it manually. However, you can integrate it numerically. So after integrating this and putting in the first equation, you obtain something like this.</p>
<p><a href="https://i.sstatic.net/NAUfz.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NAUfz.png" alt="enter image description here" /></a></p>
<p>for different <span class="math-container">$z$</span> values. In a Non-Expanding universe, we would see that as the distance (<span class="math-container">$z$</span>) increases, <span class="math-container">$d_A$</span> increases, and thus, the galaxies would appear smaller. However, that's not the case for LCDM.</p>
<p>From the graph, we can see that until a certain point, as <span class="math-container">$z$</span> increases, <span class="math-container">$d_A$</span> increases, so the galaxies appear to be smaller. However, they start to look bigger and bigger after some point as <span class="math-container">$d_A$</span> decreases.</p>
<p>As I have said, I also cannot fully grasp 'how,' but it's about the behavior of the angular diameter distance in the LCDM model.</p>

CC BY-SA 4.0
2022-05-10T06:49:19.500Z
2022-05-10T06:49:19.500Z
seVenVo1d
<p>In an expanding universe model. In addition to galaxies getting fainter with distance, they are also thought to get bigger. Thus the surface brightness of the object should decrease with distance. However, in this model why wouldn't galaxies remain the same size as its only space that's expanding between galaxies? Why are galaxies expecting to get bigger?</p>
<p>I read about this here <a href="http://www.sci-news.com/astronomy/science-universe-not-expanding-01940.html" rel="nofollow noreferrer">Universe is Not Expanding After All, Controversial Study Suggests</a></p>
<p>and in this paper <a href="https://arxiv.org/abs/astro-ph/0509611" rel="nofollow noreferrer">Evidence for a Non-Expanding Universe: Surface Brightness Data From HUDF</a>, and this more recent paper <a href="https://arxiv.org/abs/1405.0275" rel="nofollow noreferrer">UV surface brightness of galaxies from the local Universe to z ~ 5</a>.</p>

CC BY-SA 4.0
2022-02-02T00:19:01.427Z
Not gonna answer on this because I’m not totally sure, but it looks like the conclusions of the second paper are made without accounting for Malmquist Bias, which if it didn’t, would have a huge impact on the findings I think (again, not sure)
Justin T
CC BY-SA 4.0
2022-02-02T01:14:05.383Z
Have you accounted for the fact that you're not seeing the galaxy as it is today, but rather a red-shifted, delayed image of it when it was much closer?
Christopher James Huff
CC BY-SA 4.0
2022-02-03T23:52:32.683Z
The math behind the expanding universe model (the Friedmann equations) assumes that space is perfectly uniform (homogeneous & isotropic). In other words, it doesn't account for "small-scale" things like galaxies. Assuming that they expand with the rest of the universe ignores their local gravitation which resists the expansion.
D. Halsey
<expansion><hubble-constant><brightness><friedmann-equations>
Why are galaxies thought to get bigger with distance in an expanding universe model?
Tivity
# Why are galaxies thought to get bigger with distance in an expanding universe model?

(Asked by: username_0 on 2022-02-01)

In an expanding universe model. In addition to galaxies getting fainter with distance, they are also thought to get bigger. Thus the surface brightness of the object should decrease with distance. However, in this model why wouldn't galaxies remain the same size as its only space that's expanding between galaxies? Why are galaxies expecting to get bigger?

I read about this here [Universe is Not Expanding After All, Controversial Study Suggests](http://www.sci-news.com/astronomy/science-universe-not-expanding-01940.html)

and in this paper [Evidence for a Non-Expanding Universe: Surface Brightness Data From HUDF](https://arxiv.org/abs/astro-ph/0509611), and this more recent paper [UV surface brightness of galaxies from the local Universe to z ~ 5](https://arxiv.org/abs/1405.0275).

**Tags:** expansion, hubble-constant, brightness, friedmann-equations
> **Comments:**
> **username_1**: Not gonna answer on this because I’m not totally sure, but it looks like the conclusions of the second paper are made without accounting for Malmquist Bias, which if it didn’t, would have a huge impact on the findings I think (again, not sure)  
> **username_2**: Have you accounted for the fact that you're not seeing the galaxy as it is today, but rather a red-shifted, delayed image of it when it was much closer?  
> **username_3**: The math behind the expanding universe model (the Friedmann equations) assumes that space is perfectly uniform (homogeneous & isotropic). In other words, it doesn't account for "small-scale" things like galaxies. Assuming that they expand with the rest of the universe ignores their local gravitation which resists the expansion.  

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## 1 answers

### Answer by username_4 on 2022-05-10. Score: 1

It's actually due to the Angular Diameter distance. I still don't understand the exact mechanism, but I can shed some light on it. The angular diameter distance can be written as

$$d\_A = \frac{\chi}{1+z}$$

for $$\chi = c\int\_0^z \frac{dz}{H(z)}$$

In the LCDM model, this becomes

$$\chi = \frac{c}{H\_0}\int\_0^z \frac{dz}{\sqrt{\Omega\_{m,0}(1+z)^3+\Omega\_{\Lambda}}}$$

Sadly, it's nearly impossible to integrate it manually. However, you can integrate it numerically. So after integrating this and putting in the first equation, you obtain something like this.

[![enter image description here](https://i.sstatic.net/NAUfz.png)](https://i.sstatic.net/NAUfz.png)

for different $z$ values. In a Non-Expanding universe, we would see that as the distance ($z$) increases, $d\_A$ increases, and thus, the galaxies would appear smaller. However, that's not the case for LCDM.

From the graph, we can see that until a certain point, as $z$ increases, $d\_A$ increases, so the galaxies appear to be smaller. However, they start to look bigger and bigger after some point as $d\_A$ decreases.

As I have said, I also cannot fully grasp 'how,' but it's about the behavior of the angular diameter distance in the LCDM model.


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