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

Abstract

The set of homogeneous isotropic connections, as used in loop quantum cosmology, forms a line $l$ in the space of all connections $\mathcal{A}$. 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, $\overline{\mathcal{A}}$. 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.

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 (1)

• Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings

Cited by in corpus (4)

• Is loop quantization in cosmology unique?
• Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
• Fermions in Loop Quantum Cosmology and the Role of Parity
• A Cosmological Sector in Loop Quantum Gravity