Discretization parameter and operator ordering in loop quantum cosmology with the cosmological constant
- Department of Physics, Waseda University, Okubo, Tokyo 169-8555 (Japan)
- Department of Physics, Keio University, Hiyoshi, Kohoku-ku, Yokohama 223-8522 (Japan)
- Department of Physics, Rikkyo University, Toshima, Tokyo 175-8501 (Japan)
- College of Engineering, Nihon University, Koriyama 963-8642 (Japan)
In loop quantum cosmology, the Hamiltonian reduces to a finite difference operator and quantum dynamics are controlled by the difference equation. In this framework, Bojowald [M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001).] showed that the initial singularity is absent in the twofold sense: (i) the spectrum of the inverse scale factor operator is bounded from above; (ii) the wave function of the Universe can be uniquely extended beyond the point which was the initial singularity in classical theory. In this paper, we study the initial singularity in this sense and the large-volume limit against the ambiguities in the discretization and the operator ordering within a homogeneous, isotropic and spatially flat model with the cosmological constant. We find that the absence of the singularity strongly depends on the choice of the operator ordering and the requirement for the absence singles out a very small class of orderings. Moreover we find a general ordering rule required for the absence of the singularity. We also find that the large-volume limit naturally recovers a smooth wave function in the discretization where each step corresponds to a fixed volume increment but not in the one where each step corresponds to a fixed area increment. If loop quantum cosmology is to be a phenomenological realization of full loop quantum gravity, these results are important to fix the theoretical ambiguities.
- OSTI ID:
- 21502620
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 83, Issue 10; Other Information: DOI: 10.1103/PhysRevD.83.104049; (c) 2011 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Emerging singularities in the bouncing loop cosmology
Evolutionary quantum cosmology in a gauge-fixed picture