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arXiv · 0709.1621

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

Johannes Brunnemann·Christian Fleischhack
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Abstract

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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Johannes Brunnemann, Christian Fleischhack. 2009-04-24. On the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity. https://arxiv.org/abs/0709.1621

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