Abhay Ashtekar, Martin Bojowald, Jerzy Lewandowski
Mathematical Structure of Loop Quantum Cosmology
The paper is published: Adv. Theor. Math. Phys. 7 (2003) 233-268

MSC:

83C45 Quantization of the gravitational field

83F05 Cosmology

PACS: 04.60.Pp
Abstract: Applications of Riemannian quantum geometry to cosmology have had
notable successes. In particular, the fundamental discreteness
underlying quantum geometry has led to a natural resolution of the
big bang singularity. However, the precise mathematical structure
underlying loop quantum cosmology and the sense in which it
implements the full quantization program in a symmetry reduced
model has not been made explicit. The purpose of this paper is to
address these issues, thereby providing a firmer mathematical and
conceptual foundation to the subject.
Keywords: quantum geometry, loop quantum cosmology