The Mainstream Explanation
See also: Redshift, Lambda-CDM model, and metric expansion of spacePoet Edgar Allan Poe suggested that the finite size of the observable universe resolves the apparent paradox. More specifically, because the universe is finitely old and the speed of light is finite, only finitely many stars can be observed within a given volume of space visible from Earth. The density of stars within this finite volume is sufficiently low that any line of sight from Earth is unlikely to reach a star.
However, the Big Bang theory introduces a new paradox: it states that the sky was much brighter in the past, especially at the end of the recombination era, when it first became transparent. All points of the local sky at that era were brighter than the circle of the sun, due to the high temperature of the universe in that prehistoric era; and we have seen that most light rays will terminate not in a star but in the relic of the Big Bang.
This paradox is explained by the fact that the Big Bang theory also involves the expansion of space which can cause the energy of emitted light to be reduced via redshift. More specifically, the extreme levels of radiation from the Big Bang have been redshifted to microwave wavelengths (1100 times longer than its original wavelength) as a result of the cosmic expansion, and thus form the cosmic microwave background radiation. This explains the relatively low light densities present in most of our sky despite the assumed bright nature of the Big Bang. The redshift also affects light from distant stars and quasars, but the diminution is only an order of magnitude or so, since the most distant galaxies and quasars have redshifts of only around 5 to 8.6.
Read more about this topic: Olbers' Paradox
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