Quantum de Sitter algebra and some possible applications in cosmology

Abstract

I summarize results recently obtained in collaboration with Amelino-Camelia, Bruno and Mandanici (preprint University of Rome “La Sapienza”, August, 2005) that concern an analysis of the path of a massless particle in a q-de Sitter space-time and an approximation scheme suitable for the corresponding analysis in a quantum FRW Universe. On the basis of some arguments in the quantum-gravity literature, the q deformation parameter is assumed to depend on both the Planck scale and the curvature, leading to results that are significantly different from those of other studies of Planck-scale effects in cosmology, where the possibility of an interplay between curvature and Planck scale was ignored.