Just as Robert Frost imagined two possible fates for the Earth in his poem, cosmologists envision two possible fates for the universe:
The density of the universe also determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. This implies that photon paths diverge slowly and eventually return back to a point. If the density of the universe is less than the critical density, then the geometry of space is open, negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper. Thus, there is a direct link between the geometry of the universe and its fate.
The simplest version of the inflationary theory, an extension of the Big Bang theory, predicts that the density of the universe is very close to the critical density, and that the geometry of the universe is flat, like a sheet of paper.
The MAP satellite aims to measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe is open, then the cosmic microwave background fluctuations are largest on the half degree scale. If the universe is flat, the the fluctuations are largest on the degree scale. While if the universe is closed, the fluctuations are largest on even larger scale. Thus, MAP's measurement of the fluctuation scale directly probes the density of the universe and will give cosmologists insight into the ultimate fate of the universe.
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David N. Spergel / dns@astro.princeton.edu