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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

and in this paper Evidence for a Non-Expanding Universe: Surface Brightness Data From HUDF, and this more recent paper UV surface brightness of galaxies from the local Universe to z ~ 5.

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  • $\begingroup$ 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) $\endgroup$
    – Justin T
    Feb 2 at 0:19
  • $\begingroup$ 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? $\endgroup$ Feb 2 at 1:14
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    $\begingroup$ 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. $\endgroup$
    – D. Halsey
    Feb 3 at 23:52

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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

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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