## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 7, Number 2 (2003), 233-268.

### Mathematical structure of loop quantum cosmology

Abhay Ashtekar, Martin Bojowald, and Jerzy Lewandowski

#### 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.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 7, Number 2 (2003), 233-268.

**Dates**

First available in Project Euclid: 4 April 2005

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1112627633

**Mathematical Reviews number (MathSciNet)**

MR2015165

#### Citation

Ashtekar, Abhay; Bojowald, Martin; Lewandowski, Jerzy. Mathematical structure of loop quantum cosmology. Adv. Theor. Math. Phys. 7 (2003), no. 2, 233--268. https://projecteuclid.org/euclid.atmp/1112627633