Abstract
Perhaps standard effective field theory arguments are right, and vacuum fluctuations really do generate a huge cosmological constant. I show that if one does not assume homogeneity and an arrow of time at the Planck scale, a very large class of general relativistic initial data exhibit expansions, shears, and curvatures that are enormous at small scales, but quickly average to zero macroscopically. Subsequent evolution is more complex, but I argue that quantum fluctuations may preserve these properties. The resulting picture is a version of Wheeler's "spacetime foam," in which the cosmological constant produces high curvature at the Planck scale but is nearly invisible at observable scales.
Highlights
Quantum fluctuations of the vacuum are expected to generate a very high energy density, which should manifest itself as an enormous cosmological constant
If Λ is generated by Planck scale quantum fluctuations, there is no reason to expect homogeneity at that scale
Starting with the initial value formulation of general relativity with a large cosmological constant, I show that a very large class of initial data has a local Hubble constant that is huge at the Planck scale but tiny macroscopically
Summary
Quantum fluctuations of the vacuum are expected to generate a very high energy density, which should manifest itself as an enormous cosmological constant. Starting with the initial value formulation of general relativity with a large cosmological constant, I show that a very large class of initial data has a local Hubble constant that is huge at the Planck scale but tiny macroscopically. If the initial inhomogeneities are generated by quantum fluctuations, though, I argue that these fluctuations should preserve the crucial properties that camouflage the cosmological constant. These arguments do not provide a complete answer to the cosmological constant problem. They do not, for example, explain the apparent existence of a very small Λ at macroscopic scales. The results here suggest, at least, that we may have been looking for answers at the wrong scales
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