Journal
PHYSICAL REVIEW D
Volume 82, Issue 8, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.82.084012
Keywords
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Funding
- Spanish MICINN [FIS2008-06078-C03-03]
- Spanish Consolider-Ingenio 2010 Program CPAN [CSD2007-00042]
- NSF [PHY0854743]
- George A. and Margaret M. Downsbrough Endowment
- Penn State
- Le Fonds quebecois de la recherche sur la nature et les technologies
- Edward A. and Rosemary A. Mebus funds
- CSIC
- European Social Fund [I3P-BPD2006]
- Direct For Mathematical & Physical Scien
- Division Of Physics [854743] Funding Source: National Science Foundation
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We complete the quantization of the vacuum Bianchi I model within the framework of loop quantum cosmology adopting a new improved dynamics scheme put forward recently. In addition, we revisit the hybrid quantization of the Gowdy T-3 cosmologies with linear polarization using that scheme, proving with rigor some steps that remained unconcluded. The family of Gowdy T-3 cosmologies is an inhomogeneous model whose subset of homogeneous solutions is given precisely by the vacuum Bianchi I model. Our hybrid approach combines the new loop quantum cosmology description of this homogeneous sector with a Fock quantization of the inhomogeneities. Both in the Bianchi I model and in the Gowdy model the Hamiltonian constraint provides an evolution equation with respect to the volume of the Bianchi I universe, which is a discrete variable with a strictly positive minimum. We show that, in vacuo, this evolution is well defined inasmuch as the associated initial value problem is well posed: physical solutions are completely determined by the data on the initial section of constant Bianchi I volume. This fact allows us first to carry out to completion the quantization of the vacuum Bianchi I model which had not yet been achieved and then to confirm the feasibility of the hybrid procedure when the homogeneous sector is quantized with the new improved dynamics scheme.
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