The “Flatness” Problem

The “Flatness” Problem

Inflation also explains the “flatness” problem, but we first much define what this means. As
mentioned previously, the mass density of the universe controls the space-time curvature of the
universe. If the mass density is larger than a certain critical value, then space is curved in such a
way that the extent of the universe is finite, analogous to the surface area on a globe being finite.
If one could quickly traverse through the universe, one would eventually return to where one
started, but the limiting speed of light in an expanding universe does not really allow this
possibility. If the mass density is lower than this critical value, then space is curved in such a
way that the extent of the universe is infinite, analogous to what the surface of a saddle looks
like. In one direction the saddle is curved downward while in another direction the saddle is
curved upward. Continuing the saddle surface on upward and downward continuously renders a
surface that has no end. In between these two possible curvatures of the universe is a flat surface
that has neither curvature. Given the wide range of possible mass densities of the universe, it
would seem a remarkable coincidence if the universe just happened to have the mass density that
makes it completely flat, a mass density equal to the critical value. But according to our
observations, that appears to be very nearly the case.
Amazingly, inflation actually requires a nearly flat universe. The initial inflation of the universe
likely expanded the universe to such a great size beyond what the present visible extent of it
shows today, that we can only observe very little of the entire universe. If so, regardless of what
the initial curvature of the universe may have been prior to inflation, the curvature automatically
gets “flattened out” by the immense stretching or inflating of space-time, just as the surface of a
balloon seems to get flatter at any one point as the balloon expands. Thus the universe should
actually be nearly flat if indeed inflation took place as we now believe it did. And a flat spacetime
universe requires the mass density of the universe to be nearly that of the critical density of
the universe, as we’ve discussed.