The consistent histories approach to loop quantum cosmology

Abstract

We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on "measurements" to convert unrealized quantum potentialities into physical outcomes that can be assigned probabilities. In the early universe and other physical contexts in which there are no observers or measuring apparatus (or indeed, in any closed quantum system), what criteria determine which alternative outcomes may be realized and what their probabilities are? In the consistent histories formulation it is the vanishing of interference between the branch wave functions describing alternative histories -- as determined by the system's decoherence functional -- that determines which alternatives may be assigned probabilities. We describe the consistent histories formulation and how it may be applied to canonical loop quantum cosmology, describing in detail the application to homogeneous and isotropic cosmological models with scalar matter. We show how the theory may be used to make definite physical predictions in the absence of "observers". As an application, we demonstrate how the theory predicts that loop quantum models "bounce" from large volume to large volume, while conventional "Wheeler-DeWitt"-quantized universes are invariably singular. We also briefly indicate the relation to other work.

31 pages, 4 pdf figures. Invited review for special issue of Int. J. Mod. Phys. D on loop quantum cosmology. Typos corrected

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Cited by in corpus (7)

• Pre-inflationary universe in loop quantum cosmology
• Loop Quantum Cosmology: A brief review
• An elementary introduction to loop quantum gravity
• Path integral polymer propagator of relativistic and non-relativistic particles
• Loop quantum cosmology and singularities
• Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects
• The Vertex Expansion in the Consistent Histories Formulation of Spin Foam Loop Quantum Cosmology