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arXiv · 1209.4374

On the Uniqueness of Kinematics of Loop Quantum Cosmology

Abhay Ashtekar·Miguel Campiglia
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Abstract

The holonomy-flux algebra $\A$ 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 $\A$ to a much smaller algebra, $\A_{\rm Red}$, used in loop quantum cosmology. In Bianchi I models, it is shown that the requirement of covariance under \emph{residual} diffeomorphism symmetries again uniquely selects the representation of $\A_{\rm Red}$ that has been commonly used. We discuss the close parallel between the two uniqueness results and also point out a difference.

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Abhay Ashtekar, Miguel Campiglia. 2012-09-19. On the Uniqueness of Kinematics of Loop Quantum Cosmology. https://doi.org/10.1088/0264-9381%2F29%2F24%2F242001

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