Non commutative Friedmann spacetimes from Penrose-like inequalities

Abstract

In this paper a generalisation of the Doplicher-Fredenhagen-Roberts (DFR) construction of a physically motivated non commutative Minkowski spacetimeis generalised to the case of Friedmann flat expanding spacetimes. In particular, uncertainty relations quantitatively expressing limitations in the localisation of quantum observables are described and commutation relations implying them are derived from a general analysis. They reduce in a suitable sense to the DFR ones in the flat limit. Finally, it is shown that representations of these commutation relations do exist.