2002/02/21 by Martin Bojowald · 6 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #De Sitter universe #Hamiltonian (control theory) #Hamiltonian constraint #Initial singularity #Loop quantum cosmology #Loop quantum gravity #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum cosmology #Quantum gravity #Quantum mechanics #Semiclassical physics #Singularity #Theoretical physics #Universe #WKB approximation #Wheeler–DeWitt equation #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/19/10/313
published as Class.Quant.Grav. 19 (2002) 2717-2742 · 30 pages
arxiv created 2002/02/21 · openalex publication_date 2002/04/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.