Geometry and Mass
Determining the geometry of the Universe is the same as determining the total amount
of mass that it contains. In general relativity geometry and gravity are the
same thing, and mass is the source of the gravitational field. Thus, we don't yet know
the geometry of the Universe because we are not certain about the total mass of the Universe.
This is tied intimately to the dark matter problem since most of the matter of the Universe
appears to reside in dark matter.