Many people often ask how the existence of a Big Bang
can be reconciled with the possibility that we live in an infinite Universe.
Many people often ask, “Wouldn’t it take an infinite amount of time
for the Universe to expand to an infinite size, if all the mass in the Universe
started out concentrated at one point during the Big Bang?”
The key to understanding the answer to this question is to realize that there is
no “center” to the Universe from which all other points are travelling away from.
Every observer in the Universe will see all the galaxies
moving away from them as if they are at the center of expansion.
Think of all the points in the Universe as being arranged in an infinite line,
with a certain distance between each point and its two neighboring points.
This distance increases with time.
If we go backwards in time, this distance decreases.
If we go back in time all the way to the Big Bang, this distance decreases to zero.
At any time after the Big Bang, this distance is greater than zero.
The size of the universe at any time after the Big Bang is
the number of points multiplied by the distance between neighboring points.
The number of points is infinity,
and infinity multiplied by any non-zero number is also infinity.
Hence, the existence of the Big Bang does not contradict
the possibility that we live in an infinite Universe.