Deriving the Equation for the Total Vacuum Energy Density at the Planck Scale by Using the Hubble Kinetic Energy at the Planck Scale Rather Than the Planck Energy at the Planck Scale, Reproducing the Friedmann Equation for a Flat Universe, Which is a Possible Solution to the Cosmological Constant Problem

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Authors: Brian Wilkinson
Cited by: 0

Abstract

In this report, an equation for the total energy density at the Planck scale is derived, exactly reproducing the Friedmann equation for a flat universe. The Friedmann equation is a general relativity equation that calculates the total energy density based on the value of the Hubble parameter. A formula for the kinetic energy at the Planck scale is derived, which already includes the effects of both the contemporary very high value of quantum mechanics energy density and quantum gravity. The combined effects of the very high value of energy density and quantum gravity is evident from the value of the Hubble parameter, so the Hubble parameter is used as part of the calculation of the dark energy density in this report without using quantum gravity or the very high value of the quantum mechanics energy density. In reality, the value of the Hubble parameter changes at the Planck scale versus on cosmological scales. However, the Hubble parameter can still be treated as a constant, even at the Planck scale, to approximate the energy density at the Planck scale. The only difference between the derivation of energy density in this report and the derivation of energy density for the contemporary cosmological constant problem is that the contemporary cosmological constant problem uses the Planck Energy whereas the Planck kinetic energy is used in this report. If the Planck energy were used in place of the kinetic energy for the energy density derivation of this report, that would yield the 120 orders of magnitude difference in value of the energy density. The equation for the kinetic energy at the Planck scale is a little different from the kinetic energy formula that applies on cosmological scales. The Planck-Einstein relation is used for the derivation of the Planck mass in this report which is a quantum mechanics formula. The Planck mass is used to derive the energy density at the Planck scale in this report. This may be a solution to the cosmological constant problem.

Fields of Study & Subjects

Cosmology and Gravitation Theories Noncommutative and Quantum Gravity Theories Relativity and Gravitational Theory

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
19 January 2026