Author(s)

Vernon Cooray¹, Gerald Cooray², Marcos Rubinstein³, Farhad Rachidi⁴

¹Department of Electrical Engineering, Uppsala University, Uppsala, Sweden.
²Karolinska Institute, Stockholm, Sweden.
³HEIG-VD, University of Applied Sciences and Arts Western Switzerland, Yverdon-les-Bains, Switzerland.
⁴Electromagnetic Compatibility Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland.

In this paper, an inequality satisfied by the vacuum energy density of the universe is derived using an indirect and heuristic procedure. The derivation is based on a proposed thought experiment, according to which an electron is accelerated to a constant and relativistic speed at a distance L from a perfectly conducting plane. The charge of the electron is represented by a spherical charge distribution located within the Compton wavelength of the electron. Subsequently, the electron is incident on the perfect conductor giving rise to transition radiation. The energy associated with the transition radiation depends on the parameter L. It is shown that an inequality satisfied by the vacuum energy density will emerge when the length L is pushed to cosmological dimensions and the product of the radiated energy and the time duration of emission are constrained by Heisenberg’s uncertainty principle. The inequality derived is given by ρ_Λ ≤ 9.9×10^-9J/m³ where ρ_Λ is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 0.538 × 10^-9J/m. Since there is a direct relationship between the vacuum energy density and the Einstein’s cosmological constant, the inequality can be converted directly to that of the cosmological constant.

Classical Electrodynamics, Electromagnetic Radiation, Action, Radiated Energy, Photon, Heisenberg’s Uncertainty Principle, Dark Energy, Vacuum Energy, Cosmological Constant, Hubble Radius

Cooray, V. , Cooray, G. , Rubinstein, M. and Rachidi, F. (2023) Heuristic Estimation of the Vacuum Energy Density of the Universe: Part I—Analysis Based on Time Domain Electromagnetic Radiation. Journal of Electromagnetic Analysis and Applications, 15, 73-81. doi: 10.4236/jemaa.2023.156006.