On the uniqueness of kinematics of loop quantum cosmology
Abstract
The holonomy-flux algebra \mathfrak {A} 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 context, the requirement of spatial homogeneity naturally reduces \mathfrak {A} to a much smaller algebra, \mathfrak {A}_Red, used in loop quantum cosmology. In Bianchi I models, it is shown that the requirement of covariance under residual diffeomorphism symmetries again uniquely selects the representation of \mathfrak {A}_Red that has been commonly used. We discuss the close parallel between the two uniqueness results and also point out a difference.
Communicated by A Corichi- Publication:
-
Classical and Quantum Gravity
- Pub Date:
- December 2012
- DOI:
- 10.1088/0264-9381/29/24/242001
- arXiv:
- arXiv:1209.4374
- Bibcode:
- 2012CQGra..29x2001A
- Keywords:
-
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Mathematical Physics;
- Quantum Physics
- E-Print:
- 9 pages