The Cosmological Constant From Planckian Fluctuations and the Averaging Procedure

Abstract

In this paper I continue the investigation in [1,2] 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 [3] is obtained with the foliation in terms of the mean value s(t) of the time operatort in a maximally localizing state {s} of a quantum spacetime [4,5,6,7] and in a cosmological context [8]. As a result, after introducing a decoherence length scale L D where quantum fluctuations are averaged on, a classical de Sitter universe emerges with a small cosmological constant depending on L D and frozen in a true vacuum state (lowest energy), provided that the kinematical backreaction is negligible at that scale L D . Finally, I analyse the case with a non-vanishing initial spatial curvature R showing that, for a reasonable large class of models, spatial curvature and kinematical backreation Q are suppressed by the dynamical evolution of the spacetime. * viaggiu@axp.mat.uniroma2.it and s.viaggiu@unimarconi.it 1

Einstein, Planck and Vera Rubin: Relevant Encounters Between the Cosmological and the Quantum Worlds

“…Remarkably, a completely new point of view, regarding the origin of Λ has been recently put forward [221][222][223] The main idea relies on the nature of Λ and its very small observed value and states that quantum fluctuations can explain the equation of state of the cosmological constant. In fact, a radiation field sufficiently close to the Planck scale can allow quantum fluctuations so strong to permit the transformation of this radiation field into one with the equation of state that Λ shows.…”

The physical nature of the cosmological constant and the decoherence scale in a renormalization-group approach

“…The scale L D fixes the observed value of Λ. In this paper we continue the investigations in [13,14,15]. In particular, after adopting a suitable physically reasonable expression for the renormalization scale µ, we analyse the possible relation between our semiclassical expression for ρ Λ and the one extrapolated in literature by using a renormalization group approach [16,17,18,19,20,21].…”

“…With Λ we denote the actual observed value of the cosmological constant. First of all note that [13,14,15], thanks to homogeneity and isotropy of the spacetime, we can consider an arbitrary spherical region of the universe centered in an arbitrary spatial point. At Planckian scales this spherical ball will result inhomogeneous.…”

“…As a consequence, any spherical region with L ≥ L D will expand with the same factor a(t) in (1), as implied by homogeneity and isotropy. To be more quantitative, the starting point of the model presented in [13,14,15] is to consider a spherical ball of fixed proper areal radius L = a(t)r. For the aforementioned spherical ball, general relativity allows to define a quasi-local (Misner-Sharp) mass M ms , with related Misner Sharp energy given by…”

“…In [11] the cosmological constant is supposed to be effectively given by Λ ∼ 1 L 2 P at Planckian scales, but effective inhomogeneities at Planckian scales inhibit a huge cosmological constant and as a consequence a small cosmological constant emerges at macroscopic scales. In [13,14,15], we presented a new model. The new idea is that a huge cosmological constant is effectively created at Planckian scales, where Planckian fluctuations are expected to be very strong, but vacuum fluctuations must be averaged on bigger and bigger scales.…”