Einstein-Heisenberg Consistency Condition Interplay with Cosmological Constant Prediction in Resummed Quantum Gravity

Abstract

We argue that our recent success in using our resummed quantum gravity approach to Einstein's general theory of relativity, in the context of the Planck scale cosmology formulation of Bonanno and Reuter, to estimate the value of the cosmological constant Λsupports the use of quantum mechanical consistency requirements to constrain the main uncertainty in that very promising result. This main uncertainty, which is due to the uncertainty in the value of the time t_{\text{tr}} at which the transition from the Planck scale cosmology to the FRW model occurs, is shown to be reduced, by requiring consistency between the Heisenberg uncertainty principle and the known properties of the solutions of Einstein's equations, from four orders of magnitude to the level of a factor of {\cal O}(10). This lends more credibility to the over-all resummed quantum gravity approach itself, in general, and to our estimate of $Λ$ in particular.