Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies

Abstract

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lemaître 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 costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.

Final version published in Class. Quantum Grav

References in corpus (5)

• Loop Quantum Cosmology: An Overview
• Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity
• A Reformulation of the Hoop Conjecture
• Physically motivated uncertainty relations at the Planck length for an emergent non commutative spacetime
• Comment on "Can we measure structures to a precision better than the Planck length?"[arXiv:1205.3636], by Sabine Hossenfelder

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