By studying the brightness of explosions of distant Type Ia supernovae (ignited by supersoft x-ray sources), astronomers can analyze a number of different properties of the universe, including how quickly it is expanding. Several different teams of astronomers have recently found an interesting detail about the supernovae they were observing - they were on average 25% dimmer than previously expected. After correcting for possible problems with the observational process, they concluded that there are three major explanations for the discrepancy.
The first is that the distant supernovae being observed are somehow fundamentally different from the supernovae of more mature galaxies, possibly spewing less nickel or iron. However, astronomers believe this is the least likely possibility. The second is that the curvature of space is negative, or shaped like a three-dimensional saddle surface. The light would then have a greater area than it would in flat space, thus reducing the brightness of the supernova. 
However, this does not seem to be the case either - in fact, some astronomers believe that the universe is a hypersphere, and thus has positive curvature. The third and most likely explanation is that the supernovae are farther away than is suggested by their redshifts. This may imply that the universe has been expanding at a slower rate in the past that previously supposed. This, in turn, would imply an acceleration in the expansion rate of the universe, which actually means a greater age for the universe (see image).
If the expansion rate of the universe is supposed to be the minimum possible, the universe is assumed to have negative curvature, and there is assumed to be very little matter in the universe - all three extremes that seem necessary, according to the inflationary theory, to explain the supernova data - the supernova will still appear too faint for conditions. Thus, the supernova data seem to imply a radical rate of expansion that is actually accelerating with time. Under normal circumstances, this is impossible; gravity's innate attraction would invariably slow the expansion. However, with the introduction of Einstein's cosmological constant or cosmological geometry, these unusual results could be explained.
The cosmological constant is a term in Einstein's equations that describes the energy inherent in vacuum. When Einstein discovered that his equations predicted an expanding universe, he added it to adjust for the expansion, thus giving a steady and unchanging universe. When experiments confirmed the expansion, he eliminated the constant, calling it "the greatest blunder of my life." However, new research may show that Einstein was right the first time - there may actually be a cosmological constant. Although we know it is very close to zero, there is no evidence completely ruling it out, and in fact some new evidence, including that presented above, actually supports it.
Generally speaking, the universe's geometry has three possibilities: open, closed, and flat. Basically, an open universe expands forever, a closed universe contracts into a Big Crunch, and a flat universe expands at an ever-slower rate. Standard inflationary cosmology predicts a flat universe, but a catalog of observable matter reveals that there is simply not enough matter to make the universe flat. The value omega, or 
, represents the ratio of matter density (or energy density) to the density needed to make the universe flat. Obviously, a flat universe's must equal 1; however, scientists cannot detect or postulate enough matter to meet this requirement. Thus, the universe could genuinely be open, or it could have different properties than those suggested by the inflationary model.
Quantum theory and its uncertainty principle allow for the momentary existence of virtual particles. In 1967, Yakov Zeldovich, a Russian astrophysicist, showed that these virtual particles in a vacuum behave just as the cosmological constant would. However, calculations based on this idea revealed a vast discrepancy - calculating the energy associated with all these quantum particles gives an infinite result, and correcting for particles with too-small wavelengths yields a result some 10100 times greater than the observed value of close to zero. Small positive values, as implicated by experiment, would lead to a repulsive force similar to but opposite gravity. Some theorists have also proposed that the cosmological constant isn't really constant, but actually varies with time. Their main argument behind this idea is the fact that currently the values for the density of matter and the converted density represented by the cosmological constant are quite close.
Inflationary theory adds the inflaton field, associated with potential energy and acting as an antigravity that pushes space to expand rapidly. Some theories suggest that it is analogous to a ball rolling down a hill; it tries to get to the bottom of its potential. Standard inflation suggests that it started high due to quantum effects, then simply "rolled down the hill" to its minimum. However, open inflation predicts that the universe is open or saddle-shaped instead of flat. Within this framework, the inflaton field got caught in a "false minimum" and never escaped, thus inflation never ended in most of the universe. However, in some regions, it "tunneled" out of the false-minimum state (called false-vacuum decay) to the true minimum. One such region is that which we inhabit.
More specifically, false-vacuum decay happened in one location first, then spread to other early bubbles. Those smaller than a certain unknown minimum collapsed due to quantum effects, but some bubbles grew large enough to render quantum effects unimportant and thus expanded until the inflaton field returned to its descent - the moment of the big bang in other theories.
Created by Dan Corbett, Kate Stafford, and Patrick Wright for ThinkQuest.