October 2, 2000


Illustration by Flavio Robles

Once upon a time, when astronomers spoke of the universe as "closed," "open," or "flat," they meant that the density of the universe was either so great that it would eventually recollapse because of gravitational attraction; or that its density was so low that gravity would be insufficient to keep it from expanding forever; or that its density was so delicately adjusted that, eventually, it would neither expand nor contract.

"Closed," "open," and "flat" actually refer to the shape, or curvature, of space-time itself. Impossible to picture in three spatial dimensions, this is easy enough in two: two-dimensional space with positive curvature would resemble the surface of a sphere (on which parallel lines converge). Two-dimensional space with negative curvature would be like the surface of a saddle or a Pringle's potato chip (on which parallel lines diverge). A flat two-dimensional universe would resemble a sheet of paper (on which parallel lines stay parallel).

Many independent observations indicate that the universe is in fact flat. Moreover, inflation theory, the notion that a small portion of the universe briefly underwent very rapid expansion shortly after the Big Bang -- which is favored by cosmologists not least because it explains a great many otherwise puzzling things, such as the remarkable smoothness and homogeneity of regions of space that have never been in contact -- requires a flat universe.

But if the universe is flat and the density of matter is low -- including visible matter, invisible matter, and ordinary energy (which is equivalent to matter) -- something must provide the missing density. That something is the cosmological constant, or some other form of dark energy.

Such invisible energy could propel even a closed universe to eternal expansion. If the cosmological constant really is constant, the expansion of the universe will accelerate indefinitely.