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Title: Loop quantum cosmology and the k=-1 Robertson-Walker model

Abstract

The loop quantization of the negatively curved k=-1 Robertson-Walker model poses several technical challenges. We show that the issues can be overcome and a successful quantization is possible that extends the results of the k=0, +1 models in a natural fashion. We discuss the resulting dynamics and show that for a universe consisting of a massless scalar field, a bounce is predicted in the backward evolution in accordance with the results of the k=0, +1 models. We also show that the model predicts a vacuum repulsion in the high curvature regime that would lead to a bounce even for matter with vanishing energy density. We finally comment on the inverse volume modifications of loop quantum cosmology and show that, as in the k=0 model, the modifications depend sensitively on the introduction of a length scale which a priori is independent of the curvature scale or a matter energy scale.

Authors:
 [1];  [2]
  1. Institute for Gravitational Physics and Geometry, Pennsylvania State University, University Park, Pennsylvania 16802 (United States)
  2. (United Kingdom)
Publication Date:
OSTI Identifier:
20935219
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.023523; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGY; ENERGY DENSITY; GALACTIC EVOLUTION; MATTER; QUANTIZATION; QUANTUM GRAVITY; SCALAR FIELDS; UNIVERSE

Citation Formats

Vandersloot, Kevin, and Institute for Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG. Loop quantum cosmology and the k=-1 Robertson-Walker model. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.023523.
Vandersloot, Kevin, & Institute for Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG. Loop quantum cosmology and the k=-1 Robertson-Walker model. United States. doi:10.1103/PHYSREVD.75.023523.
Vandersloot, Kevin, and Institute for Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG. Mon . "Loop quantum cosmology and the k=-1 Robertson-Walker model". United States. doi:10.1103/PHYSREVD.75.023523.
@article{osti_20935219,
title = {Loop quantum cosmology and the k=-1 Robertson-Walker model},
author = {Vandersloot, Kevin and Institute for Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG},
abstractNote = {The loop quantization of the negatively curved k=-1 Robertson-Walker model poses several technical challenges. We show that the issues can be overcome and a successful quantization is possible that extends the results of the k=0, +1 models in a natural fashion. We discuss the resulting dynamics and show that for a universe consisting of a massless scalar field, a bounce is predicted in the backward evolution in accordance with the results of the k=0, +1 models. We also show that the model predicts a vacuum repulsion in the high curvature regime that would lead to a bounce even for matter with vanishing energy density. We finally comment on the inverse volume modifications of loop quantum cosmology and show that, as in the k=0 model, the modifications depend sensitively on the introduction of a length scale which a priori is independent of the curvature scale or a matter energy scale.},
doi = {10.1103/PHYSREVD.75.023523},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
  • We consider a flat cosmological model with a free massless scalar field and the cosmological constant {Lambda} in the framework of loop quantum cosmology. The scalar field plays the role of an intrinsic time. We apply the reduced phase space approach. The dynamics of the model is solved analytically. We identify elementary observables and their algebra. The compound physical observables like the volume and the energy density of matter field are analyzed. Both compound observables are bounded and oscillate in the {Lambda}<0 case. The energy density is bounded and oscillates in the {Lambda}>0 case. However, the volume is unbounded frommore » above, but periodic. The difference between standard and nonstandard loop quantum cosmology is described.« less
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  • We study the quantum vacuum definition for spin-(1/2) fields in a Robertson-Walker universe using the coincidence of a local property (singularity structure of the DeWitt-Schwinger kernel) and a global property (energy minimization) and we obtain two kinds of vacua: strong and weak (which coincide with the energy minimization vacuum). The density of particles created during the expansion of the Universe between two weak vacua is found to be finite. However, we prove that the energy-momentum tensor vacuum expectation value is nonrenormalizable.
  • The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semiclassical at some late time, the big bangmore » is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the 'difficulties' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists.« less