The INFLATION model is a theory that proposes a extremely rapid and enormous expansion of the universe in the first instants after the Big Bang.
In the instant between 10-43 and 10-35 seconds after the Big Bang, the formation of elementary particles (quarks, antiquarks, leptons, antileptons) produced an enormous amount of energy -- a sort of antigravity or pressure that caused the universe to expand tremendously. The universe then "inflated" and any irregularities in it were greatly smoothed out. This smoothing led to the situation where the geometry of the universe is flat, a specific prediction of the inflationary theory.
In the inflationary model, between 10-35 and 10-33 seconds, the "universe" doubles in size every 10-35 sec. By the end of inflation then, space-time is 1050 times bigger than it was before inflation.
Regions of "this universe" "supercool" and "nucleate" away from the rest. Perhaps "our universe" is one of these separate regions.
The WMAP satellite has determined very precisely values of the cosmological parameters, including the value of Omegatotal, the total density. WMAP's value of Omegatotal is 1.02 +/- 0.02. Within the errors then, Omegatotal is equal to 1, and the universe is flat, just as inflation requires.
The NASA MAP inflation page
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