Unitary principal series representations of the conformal group appear in the de Sitter/conformal field theory (dS/CFT) correspondence. These are infinite-dimensional irreducible representations, without highest weights. In earlier work of Güijosa and the author it was shown for the case of two-dimensional de Sitter space, there was a natural $q$-deformation of the conformal group, with $q$ a root of unity, where the unitary principal series representations become finite-dimensional cyclic unitary representations. Formulating a version of the dS/CFT correspondence using these representations can lead to a description with a finite-dimensional Hilbert space and unitary evolution. In the present work, we generalize to the case of quantum-deformed three-dimensional de Sitter spacetime and compute the entanglement entropy of a quantum field across the cosmological horizon.

• Received 16 August 2004

DOI:https://doi.org/10.1103/PhysRevD.70.104002