Isotropic loop quantum cosmology

By M. Bojowald. 2002

252 citations recorded by the source corpus.

Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely quantum geometrical effects, the classical singularity is absent in those models in the sense that the evolution does not break down there, contrary to the classical situation where spacetime is inextendible. This effect is generic and does not depend on matter violating energy conditions, but it does depend on the factor ordering of the Hamiltonian constraint. Furthermore, it is shown that loop quantum cosmology reproduces standard quantum cosmology and hence (e.g., via WKB approximation) classical behaviour in the large volume regime where the discreteness of space is insignificant. Finally, an explicit solution to the Euclidean vacuum constraint is discussed which is the unique solution with semiclassical behaviour representing quantum Euclidean space.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7942dd2dfbadb0c4d2da2531c165fa74aed8b598

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Spherically symmetric quantum geometry: Hamiltonian constraint (2005, background): “In a symmetric context, this scheme takes the form [56, 6, 8, 9] Ĥ ∝ ∑”
Effective Equations of Motion for Quantum Systems (2005, methodology): “) For details of the variables (c, p) used we refer to [14, 15].”
Loop quantum cosmology: a status report (2011, unknown): “[38–44]).”
Quantization ambiguities in isotropic quantum geometry (2002, background): “This fact has been crucial in the proof of a non-singular cosmological evolution [14, 17], so these results are insensitive to the quantization ambiguities studied here.”
Loop Quantum Cosmology (2005, background): “For non-Abelian symmetry groups integral curves as before do not form a closed loop and one needs a correction term related to intrinsic curvature components [46, 62].”
Homogeneous loop quantum cosmology (2003, methodology): “The SO(3)-matrix Λ contains purely gauge degrees of freedom and plays the same role as the matrix Λ in the isotropic decomposition [2], even though it arose in a different way.”
Inverse scale factor in isotropic quantum geometry (2001, background): “nd classical intuition cannot be trusted, but still an elucidation is needed3. This is even more important because these issues are essential for a quantum evolution through the classical singularity [15, 16]. A basic observation in this respect is that the classical value of the inverse scale facto”
Introduction to Loop Quantum Cosmology (2011, background): “In this “old quantization scheme”, the states |v〉 = |μ〉 coincide with the basis eigenstates of the momentum operator p̂, with eigenvalues v ∝ p [9, 42].”