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Why is the night sky dark?

By Love Asking Why

Set up the problem precisely. Assume the universe is infinite, eternal, and filled with stars at a roughly uniform density. Now follow any line of sight outward. The number of stars in a thin shell at distance r grows with the surface area of that shell, as r squared. The brightness of each star falls off with the same r squared. The two cancel exactly. That means every equal-thickness shell of sky contributes the same amount of light, and with infinite shells the total is infinite. Put plainly: every sightline would eventually terminate on the surface of a star, and the entire sky would glow as bright as the average stellar surface, day and night. The sky is not doing that. So at least one assumption is wrong.

Two of them are. First, the universe is not eternal. It is about 13.8 billion years old, so light has only had that long to travel, which sets a finite horizon. The number of stars along any sightline is finite, and most sightlines run out into empty space before they ever hit a star. Second, the universe is expanding, which stretches the wavelength of distant light, redshifting it out of the visible band and diluting its energy.

Here is the rigorous punchline. The sky actually is filled, in every direction, with the glow of the hot early universe. That light was emitted about 380,000 years after the beginning, when the cosmos cooled enough to become transparent, at a temperature around 3,000 kelvin, which is visible and infrared. Expansion has since redshifted it by a factor of roughly 1,100, cooling it to 2.7 kelvin: microwaves. We call it the cosmic microwave background, and instruments read it as a nearly uniform hiss across the whole sky. Olbers' blazing sky exists. It has simply been stretched below the range your eyes can see.

The darkness overhead is the finite age of the universe and the expansion of space, written where anyone can look.