Building noncommutative spacetimes at the Planck length for Friedmann flat cosmologies
Abstract
We propose physically motivated spacetime uncertainty relations (STUR) for flat FriedmannLemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we construct a concrete realization of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 September 2014
 DOI:
 10.1088/02649381/31/18/185001
 arXiv:
 arXiv:1308.2767
 Bibcode:
 2014CQGra..31r5001T
 Keywords:

 noncommutative geometry;
 Friedmann cosmologies;
 quantum spacetime;
 02.40.Gh;
 04.60.m;
 03.65.w;
 04.20.q;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 Final version published in Class. Quantum Grav