- #51

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Density is (locally) the ratio of mass to volume.

For the mass of the universe to be infinite, the local density of the universe must be (somewhere) infinite.

At the location where infinite density is to be found, the curvature of space-time (i.e. gravity) must also be infinite.

Since the space-time curvature follows an inverse-square law, if there is an infinite curvature *anywhere* there must be an infinite curvature *everywhere*.

[Infinity]/R^2 = [Infinity] for all real values of R.

There is a place where space-time curvature is finite.

Therefore space-time curvature is finite *everywhere*.