If the universe were infinite in both extent and age, what would we expect the night sky to be?

If the universe were infinite in both extent and age, one would expect the night sky to appear uniformly bright due to a concept known as Olbers' Paradox. In an infinite universe filled with an infinite number of stars, every line of sight should eventually end on a star, leading to a situation where the cumulative light from all stars would make the night sky bright.

This is because, over an infinite timescale, the light from these stars would have had sufficient time to reach Earth, filling the sky with light. The assumption here is that stars are uniformly distributed throughout the universe, which would cause every point in the sky to correspond to a celestial object.

In contrast, the night sky is not uniformly bright; it is predominantly dark with numerous stars scattered throughout. This discrepancy suggests that factors such as the finite age of the universe, the expansion of the universe, and the limited speed of light affect our observations, providing us with a mostly dark sky interspersed with stars.