On the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity

Details On the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity On the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity

2007-09-11

arxiv.org/abs/0709.1621v2

Physics

Mathematical Physics

12 pages, LaTeX. v1 to v2: Results unchanged. Presentation improved: Sect. 4 restructured (proof of Cor. 4.5 as well); some co

Scientific paper

The set of homogeneous isotropic connections, as used in loop quantum cosmology, forms a line $l$ in the space of all connections $\cal A$. This embedding, however, does not continuously extend to an embedding of the configuration space $\overline l$ of homogeneous isotropic loop quantum cosmology into that of loop quantum gravity, $\overline{\cal A}$. This follows from the fact that the parallel transports for general, non-straight paths in the base manifold do not depend almost periodically on $l$. Analogous results are given for the anisotropic case.

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