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More than 65 years ago, John Wheeler suggested that quantum uncertainties of the metric would be of order one at the Planck scale, leading to large fluctuations in spacetime geometry and topology, which he termed ‘spacetime foam.’ In this review I discuss various attempts to implement this idea and to test it, both theoretically and, to a lesser extent, observationally.
Perhaps the cosmological constant really is huge at the Planck scale, but is “hidden” by Planck scale quantum fluctuations of spacetime. I briefly review this proposal and provide some evidence, coming from a simplified midisuperspace model, that an appropriate “foamy” structure can do the job of hiding a large cosmological constant, and can persist under time evolution.
Abstract Wheeler’s conjectured ‘spacetime foam’—large quantum fluctuations of spacetime at the Planck scale—could have important implications for quantum gravity, perhaps even explaining why the cosmological constant seems so small. Here I explore this problem in a midisuperspace model consisting of metrics with local spherical symmetry. Classically, an infinite class of ‘foamy’ initial data can be constructed, in which cancellations between expanding and contracting regions lead to a small average expansion even if Λ is large. Quantum mechanically, the model admits corresponding stationary states, for which the probability current is also nearly zero. These states appear to describe a self-reproducing spacetime foam with very small average expansion, effectively hiding the cosmological constant.