On the Uniqueness of Kinematics of Loop Quantum Cosmology

TL;DR

This paper demonstrates the uniqueness of the quantum kinematic representation in loop quantum cosmology, paralleling the known uniqueness in loop quantum gravity, and discusses the implications of residual symmetries.

Contribution

It establishes a uniqueness result for the representation of the reduced holonomy-flux algebra in Bianchi I models, extending the known quantum uniqueness to cosmological settings.

Findings

Uniqueness of the representation in loop quantum cosmology is shown.

Residual diffeomorphism invariance uniquely determines the algebra's representation.

Parallel between quantum gravity and cosmology uniqueness results is discussed.

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.