# Infinities

Q:
If the universe is flat, it means it is infinite. If the Big Bang happened everywhere, then logically the Big Bang created an infinite amount of matter since it happened in an infinite space. If there is an infinite amount of matter (stars, nebulae), then there is an infinite number of gravitational fields occupying every bit of space in the universe. If we follow the logic, then space should be curved and wrapped back on itself making it a closed universe because of those infinites gravitational fields... Either my logic is wrong somewhere, or we do not really understand what the universe is really is...
- Anonymous
A:
There is an error in your logic. Let's say (we don't really know) that the universe is infinite. That means that the average curvature must be zero or negative. Positive curvature would mean, as you say, that the space would wrap around and be finite.

The curvature comes from mass density (positive), dark energy density (negative), and the expansion rate (negative). Even if there were no dark energy, a universe expanding rapidly enough would be infinite.

So where was the error in your logic? In an infinite universe an infinite total amount of mass could still give a finite density, the mass to volume ratio. Having infinity in a numerator doesn't have to give infinity in the ratio, because the denominator is infinite.

Mike W.

(published on 11/04/2010)

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