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  Loop quantum cosmology with self-dual variables

Wilson-Ewing, E. (2015). Loop quantum cosmology with self-dual variables. Physical Review D, 92(12): 123536. doi:10.1103/PhysRevD.92.123536.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0026-A16A-B Version Permalink: http://hdl.handle.net/21.11116/0000-0002-9A0A-6
Genre: Journal Article

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 Creators:
Wilson-Ewing, Edward1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
 Abstract: Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular measure for the inner product in the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well-defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomy-like operators, some of which are well-defined; these operators in turn are used in the definition of a Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum dynamics are similar, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived, which provide a good approximation to the full quantum dynamics for sharply-peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a non-singular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.

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 Dates: 2015-03-262015
 Publication Status: Published in print
 Pages: 10 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1503.07855
DOI: 10.1103/PhysRevD.92.123536
 Degree: -

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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 92 (12) Sequence Number: 123536 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258