Problems with an Infinite Universe

The problem of the night sky being dark was a problem for scientists in the past. Before modern cosmology, 2 assumptions were commonly made about the universe. One, the universe is infinite in extent and second, the universe has existed forever. Olber's paradox demonstrated that at least one of these assumptions must be incorrect. An universe both infinitely old and infinitely large would result in a night sky as bright as the sun.Modern cosmology solves the paradox in two ways. One, the universe is expanding. This means that even if the universe has been around forever, light will not be able to reach every region, even in an infinite amount of time. As well, modern cosmology suggests the universe has not existed forever, but had a beginning. Either case offers a solution to the paradox, but it just so happens both are in effect.

It's not something that has been resolved. The evidence is consistent with both - though cosmologists tend to lean towards an infinite universe for simplicity.If the universe is infinite, the big bang represents a situation where the density of each point space becomes infinite.

But this singularity is not a single point of infinite density, but infinite density throughout all of space.

Besides, Olber's paradox hasn't been a serious argument against an infinite universe for over 50 years. Modern cosmology has refuted the paradox, end of story.