Why is the sky dark if there are billions of stars in the Universe?

Billions of stars
The dark night sky paradox, often called Olbers’ paradox, named after Heinrich Wilhelm Olbers(a German physicist of the early 19th century), arises from the fact that the number of stars in the sky is assumed to be essentially infinite, and hence the night time sky should be ablaze with light, not shrouded in darkness.
If the logic were correct, no matter where we looked in the sky, the canopy of stars would be continuous, with no dark gaps between any two stars. The result would be a heavenly vault as dazzlingly bright and as hot as the Sun’s surface. A paradox arises from the seeming conflict between logic and the observed darkness of the night sky. The solution comes from the landmark cosmological discovery made by American astronomer Edwin Hubble. He demonstrated that the universe is expanding and the light from the receding galaxies is shifting towards the red end of the spectrum–just short of becoming invisible.
It follows from this that beyond a certain distance, any star or galaxy will be receding from us so rapidly that its light will be shifted out of the visible spectrum into the infrared or radio spectrum. The radiation we receive from celestial body is therefore no longer visible to our eyes. This would greatly reduce the number of stars and galaxies visible in the sky, and could explain nighttime darkness. Scientists agree that this red shifting must contribute to the darkness of the night sky.
There is another supportive explanation based on the fact that the speed of light always remains constant and it can not be boosted any further. One consequence of the fixed speed of light is that we can not observe any object farther than about 15 billion light-years away from Earth. Even if there are more galaxies beyond that distance, light from them would not have the time to reach us.

Additional reading:
Olbers’ paradox (Wikipedia)

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