Page "Olbers' paradox" Paragraph 20

Suppose that the universe were not expanding, and always had the same stellar density ; then the temperature of the universe would continually increase as the stars put out more radiation.

Eventually, it would reach 3000K ( corresponding to a typical photon energy of 0. 3 eV and so a frequency of 7. 5 × 10 < sup > 13 </ sup > Hz ), and the photons would begin to be absorbed by the hydrogen plasma filling most of the universe, rendering outer space opaque.

This maximal radiation density corresponds to about eV / m < sup > 3 </ sup > =, which is nearly eleven orders of magnitude greater than the observed value of.

So the sky is about fifty billion times darker than it would be if the universe were neither expanding nor too young to have reached equilibrium yet.