lated with virtual particles and symmetry-breaking condensates. One might think all this structure would contain energy. The definition of zero energy can be arbitrarily adjusted in many theories, but once the adjustment is made in one epoch of the universe it cannot be altered. One would therefore expect the effects of quantum corrections to give a vacuum energy in all epochs. Indeed, as argued above, this can account for the early inflationary epoch. Straightforward estimates of the expected scale of this energy in the present epoch give values far in excess of what is allowed experimentally. This is called the problem of the cosmological constant, because the mathematical description of the energy of the vacuum is equivalent to the cosmological constant originally introduced by Einstein to keep the universe from expanding or contracting. The discrepancy, depending on how the estimates are made, is at least a factor of 1055, and indicates a major gap in understanding of the vacuum and gravity.

Until very recently, it seemed reasonable to hope that some yet-undiscovered symmetry would require that all the sources of energy must cancel, so that empty space would have exactly zero energy today. But recent measurements indicate that the energy of the vacuum, while absurdly small compared with the theoretical estimates mentioned above, is not zero (see Chapter 4). Indeed, it seems to contribute about twice as much to the average energy density of the universe as all matter (ordinary plus “dark”). For the other problems mentioned here, physicists have identified some very promising lines of attack. But for the cosmological constant problem, some fundamentally new idea seems required.

Many of the challenging questions today could not even be formulated only a few years ago. The experimental and observational data and techniques at hand today are beginning to provide access to information directly relevant to our questions. Rapid progress toward better data can be anticipated. It is an exciting time for this area of science, which has blossomed through the overlapping interests of physics and astronomy.

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