A theoretical calculation of the cosmological constant based on a mechanical model of vacuum

TL;DR

This paper presents a theoretical model of vacuum involving two substrata, deriving a formula for the cosmological constant and suggesting these substrata as dark energy candidates, challenging traditional energy source assumptions in Einstein's equations.

Contribution

It introduces a new vacuum model with two substrata and derives a theoretical value for the cosmological constant, offering a novel approach to dark energy and the cosmological constant problem.

Findings

Derived a theoretical value for the cosmological constant.

Proposed the $ ext{Ω}(1)$ and $ ext{Ω}(2)$ substrata as dark energy candidates.

Challenged the inclusion of electromagnetic zero-point energy as a source in Einstein's equations.

Abstract

Lord Kelvin believed that the electromagnetic aether must also generate gravity. Presently, we have no methods to determine the density of the electromagnetic aether, or we say the $\Omega(1)$ substratum. Thus, we also suppose that vacuum is filled with another kind of continuously distributed substance, which may be called the $\Omega(2)$ substratum. Based on a theorem of V. Fock on the mass tensor of a fluid, the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substrata are established. Quasi-static solutions of the gravitational field equations in vacuum are obtained. Based on an assumption, relationships between the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substrata and the contravariant metric tensor are obtained. Thus, the cosmological constant is calculated theoretically. The $\Omega(1)$ and $\Omega(2)$ substrata may be a possible candidate of the dark energy. According to the theory of vacuum mechanics, only those energy-momentum tensors of discrete or continuously distributed sinks in the $\Omega(0)$ substratum are permitted to act as the source terms in the generalized Einstein's equations. Thus, the zero-point energy of electromagnetic fields is not qualified for a source term in the generalized Einstein's equations. Some people believed that all kinds of energies should act as source terms in the Einstein's equations. It may be this unwarranted belief that leads to the cosmological constant problem. The mass density of the $\Omega(1)$ and $\Omega(2)$ substrata is equivalent to that of around $3$ protons contained in a box with a volume of $1$ cubic metre.