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The Flatness Problem

Our universe is apparently flat. That is, it appears to have just the "right" density--or nearly so--to continue its slow expansion forever. Too much matter, and the universe eventually collapses in on itself under the influence of its own gravitational pull. This scenario, essentially the Big Bang in reverse, has been called the "Big Crunch". Too little matter, and gravity will never be able to halt the expansion of the universe. The universe eventually be populated only by gas, dust and the relics of stars, growing increasingly cold with its infinite expansion. This bleak scenario is called the Big Chill.

An intermediate scenario happens if the average density of our universe is equal to the critical density--the average density of matter needed to arrest the expansion of the universe without bringing about a Big Crunch. Cosmologists express this relationship as the ratio of the average density to the critical density: Omega. Measurements of Omega today range from 0.1 to 1. Most scientists believe that the universe is not headed for a Big Crunch.

Both the average density of the universe and the critical density change with time. When the universe was very young, and very dense, these numbers changed very rapidly. If the average density of the universe were even slightly greater or smaller than the critical density in the instant following the Big Bang, Omega would have zoomed to infinity (a quick Big Chill) or crashed to zero (the Big Crunch). The fact that we are still around, approximately 15 billion years later, is evidence that the critical density must have been extremely close--equal within 1 part in 10^15--to one after the Big Bang.

Inflation Flattens the Universe

To make the Standard Big Bang theory correspond to reality, cosmologists had to make the assumption that the average density of the universe was equal to the density immediately following the Big Bang. But how? This assumption, like the isotropy assumption, isn't explained. Since an Omega of one corresponds to a flat universe, this is known as "The Flatness Problem."
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Inflation comes to the rescue again. Inflation's rapid expansion caused space to become flatter, forcing omega toward one, no matter what its initial value. Even if the pre-inflation universe were curved like a sphere (corresponding to Omega > 1) or hyperbolic (Omega < 1), that tremendous burst of expansion forced the scale of any curvature to flatness, just as our Illinois soybean fields appear flat on a curved earth.

Although the estimated values of Omega hover around one, the range implies a lot of uncertainty about the average density of the universe. Part of the problem lies in the fact that we can only see a mere 5-10% of the matter that's thought to comprise the cosmos. The rest is mysterious "dark matter" whose presence is inferred from the gravitational motions of galaxies. We just don't know how much dark matter is out there.

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Copyright, (c) 1995: Board of Trustees, University of Illinois

NCSA. Last modified 11/2/95.