How Does a Setting of the Vacuum Energy Density, as Given Today, Lead to an Initial Hubble Radius for the Early Universe, i.e. How Does the Early Universe Partly Mimic a Black Hole?

Abstract

First we review what was done by Klauber, in his quantum field theory calculation of the Vacuum energy density, and in doing so, use, instead of Planck Mass, which has 1019 GeV, which leads to an answer 10122 times too large, a cut-off value of instead, a number, N, of gravitons, times graviton mass (assumed to be about 10°43 GeV) to get a number, N, count of about 1031 if the vacuum energy is to avoid an overshoot of 10122, and instead have a vacuum energy 10°47 GeV4. Afterwards, we use the results of Mueller and Lousto, to compare the number N, of 1031, assumed to be entropy using Ng’s infinite quantum statistics, to the ratio of the square of (the Hubble (observational) radius over a calculated grid size which we call a), here, a ~ a minimum time step we call delta t, times, the speed of light. Now in doing so, we use a root finder procedure to obtain where we use an inflaton value due to use of a scale factor if we furthermore use as the variation of the time component of the metric tensor in Pre-Planckian Space-time up to the Planckian space-time initial values.