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Title: Loop quantum cosmology of Bianchi type IX models

Abstract

The loop quantum cosmology 'improved dynamics' of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.

Authors:
 [1]
  1. Institute for Gravitation and the Cosmos, Physics Department, Pennsylvania State University, University Park, Pennsylvania 16802 (United States)
Publication Date:
OSTI Identifier:
21420914
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 82; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.82.043508; (c) 2010 American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CORRECTIONS; COSMOLOGY; EQUATIONS OF MOTION; HAMILTONIANS; QUANTUM GRAVITY; SIMULATION; SINGULARITY; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD THEORIES; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM FIELD THEORY; QUANTUM OPERATORS

Citation Formats

Wilson-Ewing, Edward. Loop quantum cosmology of Bianchi type IX models. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.82.043508.
Wilson-Ewing, Edward. Loop quantum cosmology of Bianchi type IX models. United States. doi:10.1103/PHYSREVD.82.043508.
Wilson-Ewing, Edward. 2010. "Loop quantum cosmology of Bianchi type IX models". United States. doi:10.1103/PHYSREVD.82.043508.
@article{osti_21420914,
title = {Loop quantum cosmology of Bianchi type IX models},
author = {Wilson-Ewing, Edward},
abstractNote = {The loop quantum cosmology 'improved dynamics' of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.},
doi = {10.1103/PHYSREVD.82.043508},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 82,
place = {United States},
year = 2010,
month = 8
}
  • The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved strategies are applied and the expected results are established: (i) the scalar field again serves as an internal clock and is treated as emergent time; (ii) the total Hamiltonian constraint is derived by imposing the fundamental discreteness and gives the evolution as a difference equation; and (iii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously. It is also shown that themore » state in the kinematical Hilbert space associated with the classical singularity is decoupled in the difference evolution equation, indicating that the big bounce may take place when any of the area scales undergoes the vanishing behavior. The investigation affirms the robustness of the framework used in the isotropic model by enlarging its domain of validity and provides foundations to conduct the detailed numerical analysis.« less
  • The ''improved dynamics'' of loop quantum cosmology is extended to include anisotropies of the Bianchi type I model. As in the isotropic case, a massless scalar field serves as a relational time parameter. However, the extension is nontrivial because one has to face several conceptual subtleties as well as technical difficulties. These include a better understanding of the relation between loop quantum gravity and loop quantum cosmology, handling novel features associated with the nonlocal field strength operator in presence of anisotropies, and finding dynamical variables that make the action of the Hamiltonian constraint manageable. Our analysis provides a conceptually completemore » description that overcomes limitations of earlier works. We again find that the big-bang singularity is resolved by quantum geometry effects but, because of the presence of Weyl curvature, Planck scale physics is now much richer than in the isotropic case. Since the Bianchi I models play a key role in the Belinskii, Khalatnikov, Lifshitz conjecture on the nature of generic spacelike singularities in general relativity, the quantum dynamics of Bianchi I cosmologies is likely to provide considerable intuition about the fate of generic spacelike singularities in quantum gravity. Finally, we show that the quantum dynamics of Bianchi I cosmologies projects down exactly to that of the Friedmann model. This opens a new avenue to relate more complicated models to simpler ones, thereby providing a new tool to relate the quantum dynamics of loop quantum gravity to that of loop quantum cosmology.« less
  • In homogeneous and isotropic loop quantum cosmology, gravity can behave repulsively at Planckian energy densities leading to the replacement of the big bang singularity with a big bounce. Yet in any bouncing scenario it is important to include nonlinear effects from anisotropies which typically grow during the collapsing phase. We investigate the dynamics of a Bianchi I anisotropic model within the framework of loop quantum cosmology. Using effective semiclassical equations of motion to study the dynamics, we show that the big bounce is still predicted with only differences in detail arising from the inclusion of anisotropies. We show that themore » anisotropic shear term grows during the collapsing phase, but remains finite through the bounce. Immediately following the bounce, the anisotropies decay and with the inclusion of matter with equation of state w<+1, the universe isotropizes in the expanding phase.« less
  • The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to 3 times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamicsmore » is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.« less
  • A simplified theory of the diagonal Bianchi type I model coupled with a massless scalar field in loop quantum cosmology is constructed according to the {mu} scheme. Kinematical and physical sectors of the theory are under good analytical control as well as the scalar constraint operator. Although it is possible to compute numerically the nonsingular evolution of the three gravitational degrees of freedom, the naive implementation of the {mu} scheme to the diagonal Bianchi type I model is problematic. The lack of the full invariance of the theory with respect to the fiducial cell and fiducial metric scaling causes seriousmore » problems in the semiclassical limit of the theory. Because of this behavior it is very difficult to extract reasonable physics from the model. The weaknesses of the implementation of the {mu} scheme to the Bianchi I model do not imply limitations of the {mu} scheme in the isotropic case.« less