speeding up, and not slowing down as expected. This result implies the existence of large amounts of “dark energy” whose gravitational force is repulsive (see Box 5.1).

Perhaps the biggest puzzle of all is the odd mix that makes up our universe—ordinary matter, exotic dark matter, and dark energy, all in significant amounts. This odd arrangement may imply, as the Ptolemaic epicycles did, that we are lacking a deep enough understanding of the laws of physics underlying our universe. It is even possible that what we call dark matter and dark energy are the signatures of some unknown aspect of gravity or space-time itself.

The Universe Is Flat

According to Einstein’s theory of general relativity, the total density of matter and energy (mass or energy per unit volume) in the universe determines the spatial curvature of the universe (see Box 5.2). For one density— the so-called critical density—the universe is uncurved (“flat”) and the geometry is just that of Euclid. A supercritical (closed) universe curves back on itself (like the surface of a balloon, only in all three dimensions rather than two), and a subcritical (open) universe is curved away from itself, like a saddle. The contributions to the composition of the universe mentioned above sum to a value close to the critical density, indicating a flat universe.

The cosmic microwave background (CMB) can also be used to determine the shape of the universe and thereby provide an independent accounting of the total amount of matter and energy. The angular size of the hot and cold spots in the microwave background is directly related to the shape of the universe—in a closed universe the hot and cold spots appear larger than in a flat or open universe, because the overall curvature of space acts as a cosmic lens, magnifying or demagnifying the spots (see Figure 5.1). Researchers have recently made spectacular progress with the measurement of the angular scale of the hot and cold spots on the CMB. The BOOMERanG, MAXIMA, and DASI experiments have confirmed indications from earlier experiments that the universe is indeed flat, which implies a density deviating from the critical density by at most 6 percent.

These CMB experiments not only have determined the shape of the universe but also have provided an important cross-check on the accounting of the composition of the universe. Future CMB experiments, including the MAP and the Planck satellite missions, should reveal important clues about the nature of the dark matter and dark energy. However, more experiments will ultimately be needed to clarify the nature of both.

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