On the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity
arXiv:0709.1621
Abstract
The set of homogeneous isotropic connections, as used in loop quantum cosmology, forms a line in the space of all connections . This embedding, however, does not continuously extend to an embedding of the configuration space of homogeneous isotropic loop quantum cosmology into that of loop quantum gravity, . This follows from the fact that the parallel transports for general, non-straight paths in the base manifold do not depend almost periodically on . Analogous results are given for the anisotropic case.
12 pages, LaTeX. v1 to v2: Results unchanged. Presentation improved: Sect. 4 restructured (proof of Cor. 4.5 as well); some comments added; reference updated
References in corpus (3)
Cited by in corpus (19)
- Loop Quantum Cosmology: A Status Report
- Is loop quantization in cosmology unique?
- Testing loop quantum cosmology
- Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
- Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
- Phenomenological implications of modified loop cosmologies: an overview
- Fermions in Loop Quantum Cosmology and the Role of Parity
- Minisuperspace models as infrared contributions
- Symmetry Reduction of Loop Quantum Gravity
- New Loop Quantum Cosmology Modifications from Gauge-covariant Fluxes
- Observations on interfacing loop quantum gravity with cosmology
- Configuration Spaces in Fundamental Physics
- Invariant Connections in Loop Quantum Gravity
- Piecewise linear loop quantum gravity
- Loop Quantum Gravity and Cosmology: A dynamical introduction
- A Cosmological Sector in Loop Quantum Gravity
- Projective Structures in Loop Quantum Cosmology
- Loop quantum cosmology and its gauge-covariant avatar: a weak curvature relationship
- Uniqueness of Measures in Loop Quantum Cosmology