Galaxy counts and the expansion of the universe

[bojibridge]

Homework Statement

You want to count all the galaxies out to a certain distance R(naught). If the universe were not expanding, then N (number of galaxies) would be proportional to R^3. Justify/derive.

For an expanding universe, take into account the finite time that light takes to reach us and just describe (without derivation) the relation that would be observed between N and R.

Homework Equations

The Attempt at a Solution

Is this as simple as saying that the density is mass/volume, so the more volume of space you have, the more galaxies you have? That seems to easy for this class...

 

[Dick]

Number is equal to density times volume is fine. So if the universe were not expanding R^3 is a good factor. But if it is, as you look back in time, not only is R^3 increasing the density is increasing, isn't it?