I have read this question:
The short answer to this is: We see less stars with time, due to the fact that cosmic expansion is accelerating. Although what we really see at the relevant distances are galaxies; single stars are far too far away to be resolved.
And this one:
Furthermore, over time, you are entirely correct in the assertion that the number of observable objects will increase drastically, and quite possibly infinitely. Consider that we only see x distance away which terminates at the CMB, thus limiting the number of galaxies we can see, with the furthest galaxies being the earliest evolutionary stage of galaxies. The number of "young" galaxies we can see will progressively increase as more of the veil from the CMB is pulled back through the arrival of the new light. The "young" galaxies we can see now will mature and the total number will increase.
I believe the answer is not trivial, because naively thinking, space expanding inbetween our galaxy and other galaxies, those galaxies far away should recede from us at an accelerating rate, thus eventually all disappear from our observable universe. Though, the second answer explains the opposite. My question is not just simply about stars or other objects, but specifically galaxies.
There is yet another answer, which focuses not only simply on accelerating expansion, but on redshift:
As the Universe expands, more objects pop into view, since that "horizon distance" is continually getting bigger, at least in principle. In fact, though, that's a very small effect and would not lead to the night sky becoming brighter in practice. In a practical sense, our ability to see faraway objects actually decreases with time: although in principle our horizon grows, the redshift causes any given object to become unobservably faint much faster than the rate at which new stuff is brought in across the horizon.
- Will we see more or fewer galaxies because of accelerating space expansion?