q-deformed de Sitter/conformal field theory correspondence

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 Gueijosa 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