Deformed Special Relativity as an effective flat limit of quantum gravity

Abstract

We argue that a (slightly) curved space-time probed with a finite resolution, equivalently a finite minimal length, is effectively described by a flat non-commutative space-time. More precisely, a small cosmological constant (so a constant curvature) leads the kappa-deformed Poincar\'e flat space-time of deformed special relativity (DSR) theories. This point of view eventually helps understanding some puzzling features of DSR. It also explains how DSR can be considered as an effective flat (low energy) limit of a (true) quantum gravity theory. This point of view leads us to consider a possible generalization of DSR to arbitrary curvature in momentum space and to speculate about a possible formulation of an effective quantum gravity model in these terms. It also leads us to suggest a {\it doubly deformed special relativity} framework for describing particle kinematics in an effective low energy description of quantum gravity.