# galaxies in a specific radius in different shapes of universe

Let the distribution of galaxies be a number like $n$. we want to find the total number of galaxies within the radius $r$ from a specified point. in which shape of the universe (flat, open, closed) the number we get is higher? ($n,r$ are the same in this universes and only the area (volume) in each universe is different).

• By distribution do you mean something like the number density? I don't see how you can represent "the distribution of galaxies" by a single number otherwise. – zephyr Jul 20 '17 at 18:51
• @zephyr . yes I mean number density. I want to find for example for r = 500 MPc, In which type of universe the total number of galaxies are higher? – titansarus Jul 20 '17 at 20:48
• As a hint, do you have equations that allow you to calculate distances in the universe that depend on the curvature? Usually it will depend on either $k$ or $\Omega_k$. – zephyr Jul 20 '17 at 20:55
• So what else changes between your three universes? Or are we allowed to assign arbitrary values for $\Omega_m$, $\Omega_\lambda$, $H_0$ etc.? I'm a bit rusty with the Friedmann equations, but I'm quite sure you need to provide some more information for a meaningful answer. – Alex Jul 20 '17 at 21:15

$$D_M = (1+z)^{-1} \begin{cases} \frac{1}{\sqrt{\Omega_k}}\sinh\left(\sqrt{\Omega_k}D_c/D_H\right), & k = -1 \\ D_c, & k = 0 \\ \frac{1}{\sqrt{\left|\Omega_k\right|}}\sin\left(\sqrt{\left|\Omega_k\right|}D_c/D_H\right), & k = +1 \\ \end{cases}$$
In this case, you can see the three forms it takes for a closed universe ($k=-1$), a flat universe ($k=0$), and an open universe ($k=+1$). It should be pretty clear that if you chose some volume with some radius calculated by $D_A$, you'd get different volume sizes and thus different amounts of galaxies in each volume for the three universe types.