Quantum electrodynamic fields possess fluctuations corresponding to transient particle-antiparticle dipoles, which can be characterized by a nonvanishing polarizability density. Here, we extend a recently proposed quantum scaling law to describe the volumetric and radial polarizability density of a quantum field corresponding to electrons and positrons and derive the Casimir self-interaction energy (SIE) density of the field, ${\overline{E}}_{\mathrm{SIE}}$, in terms of the fine-structure constant. The proposed model obeys the cosmological equation of state $w=-1$ and the magnitude of the calculated ${\overline{E}}_{\mathrm{SIE}}$ lies in between the two recent measurements of the cosmological constant $\mathrm{\Lambda }$ obtained by the Planck Mission and the Hubble Space Telescope.

• Received 8 March 2022
• Revised 21 August 2022
• Accepted 20 December 2022

DOI:https://doi.org/10.1103/PhysRevLett.130.041601

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Published by the American Physical Society