# Mathematical structure of loop quantum cosmology

@article{Ashtekar2003MathematicalSO, title={Mathematical structure of loop quantum cosmology}, author={Abhay Ashtekar and Martin Bojowald and Jerzy Lewandowski}, journal={Advances in Theoretical and Mathematical Physics}, year={2003}, volume={7}, pages={233-268} }

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…

## 683 Citations

On the physical Hilbert space of loop quantum cosmology

- Physics, Mathematics
- 2005

In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization.…

Quantum-Reduced Loop Gravity: Cosmology

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- 2013

We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full…

Kinematical Foundations of Loop Quantum Cosmology

- Physics
- 2016

First, we review the C∗-algebraic foundations of loop quantization, in particular, the construction of quantum configuration spaces and the implementation of symmetries. Then, we apply these results…

N ov 2 00 4 On the Physical Hilbert Space of Loop Quantum Cosmology

- Physics, Mathematics
- 2004

Abstract In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic…

The quantum configuration space of loop quantum cosmology

- Physics
- 2007

This paper gives an account of several aspects of the space known as the Bohr compactification of the line, featuring as the quantum configuration space in loop quantum cosmology, as well as of the…

On the uniqueness of kinematics of loop quantum cosmology

- Mathematics
- 2012

The holonomy-flux algebra of loop quantum gravity is known to admit a natural representation that is uniquely singled out by the requirement of covariance under spatial diffeomorphisms. In the…

Cosmological applications of loop quantum gravity

- Physics, Philosophy
- 2003

After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop…

Loop quantum modified gravity and its cosmological application

- Physics
- 2013

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical…

Non‐standard loop quantum cosmology

- Physics
- 2010

We present results concerning the nature of the cosmological big bounce (BB) transition within the loop geometry underlying loop quantum cosmology (LQC). Our canonical quantization method is an…

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