Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Derivation of Zeldovich’s Formula and Weinberg’s Relation of the Cosmological Constant Based on a Liquid Droplet Model of Electron

Version 1 : Received: 14 January 2023 / Approved: 17 January 2023 / Online: 17 January 2023 (07:22:00 CET)

How to cite: Wang, X. Derivation of Zeldovich’s Formula and Weinberg’s Relation of the Cosmological Constant Based on a Liquid Droplet Model of Electron. Preprints 2023, 2023010298. https://doi.org/10.20944/preprints202301.0298.v1 Wang, X. Derivation of Zeldovich’s Formula and Weinberg’s Relation of the Cosmological Constant Based on a Liquid Droplet Model of Electron. Preprints 2023, 2023010298. https://doi.org/10.20944/preprints202301.0298.v1

Abstract

Inspired by Dirac's large number hypothesis (LNH), Zeldovich proposed a relation between the cosmological constant (CC), the mass of a proton, the Planck constant and Newton's gravitational constant. Zeldovich's formula suggests that the substance which is responsible for CC may interact with elementary particles. Since Newton's gravitational constant and the Planck constant appear in Zeldovich's formula, these interactions may be related to gravitational phenomena and quantum phenomena. Following this clue, we propose a liquid droplet model of electron. Applying the Laplace's equation, Zeldovich's formula of CC is derived. Weinberg proposes a relation between the mass of a pion, the Planck constant, the Hubble constant, Newton's gravitational constant and the velocity of light in vacuum when discussing cosmological models with a varying constant of gravitation. Weinberg pointed out that this relation may not merely be regarded as a meaningless random combinations of these fundamental constants in physics. The Weinberg's relation is derived based on the critical mass density formula in the Friedmann model of the universe and Zeldovich's formula.

Keywords

Zeldovich's formula; Weinberg's relation; cosmological constant; dark energy; droplet; surface tension

Subject

Physical Sciences, Space Science

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