We’ve observed that the universe is expanding, and this expansion is accelerating. We know this because of the Doppler effect. Basically, when something moves quickly away from you, the wavelength of their light gets stretched, giving off a red-ish appearence. We can use this red shift to figure out roughly how fast the universe is expanding. If the universe is expanding now, perhaps it’s always been expanding, so we work backwards to predict how long it would’ve taken for the universe to go from 0 size to how it is today.
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