Foundations of Physics

, Volume 41, Issue 3, pp 371–379 | Cite as

Consistent Histories in Quantum Cosmology



We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models.


Quantum cosmology Minisuperspace Decoherence Consistent histories 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of PhysicsLe Moyne CollegeSyracuseUSA
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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