Abstract

In this paper I continue the investigation in Viaggiu, Viaggiu concerning my proposal on the nature of the cosmological constant. In particular, I study both mathematically and physically the quantum Planckian context and I provide, in order to depict quantum fluctuations and in absence of a complete quantum gravity theory, a semiclassical solution where an effective inhomogeneous metric at Planckian scales or above is averaged. In such a framework, a generalization of the well known Buchert formalism is obtained with the foliation in terms of the mean value \\) of the time operator \ in a maximally localizing state \ of a quantum spacetime and in a cosmological context. As a result, after introducing a decoherence length scale \ where quantum fluctuations are averaged on, a classical de Sitter universe emerges with a small cosmological constant depending on \ and frozen in a true vacuum state, provided that the kinematical backreaction is negligible at that scale \. Finally, I analyse the case with a non-vanishing initial spatial curvature \ showing that, for a reasonable large class of models, spatial curvature and kinematical backreation \ are suppressed by the dynamical evolution of the spacetime.