Building non commutative spacetimes at the Planck length for Friedmann
  flat cosmologies
  We propose physically motivated spacetime uncertainty relations (STUR) for
flat Friedmann-Lema\^{i}tre 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.
