The Gravitational-Electromagnetic Analogy: A Possible Solution to the Vacuum-Energy and Dark-Energy Problems

TL;DR

This paper explores a gravitational-electromagnetic analogy via curvature equations, proposing a reinterpretation of general relativity that addresses the vacuum-energy and dark-energy problems in cosmology.

Contribution

It introduces a reinterpretation of Einstein's equations using curvature equations, offering a potential solution to the vacuum-energy and dark-energy issues.

Findings

The effective cosmological constant energy density is vastly smaller than quantum vacuum energy estimates.

Quantum vacuum energy does not act as a source of curvature in this framework.

The curvature equations resemble Maxwell's equations, suggesting a unified pattern for fundamental forces.

Abstract

There is a set of first-order differential equations for the curvature tensor in general relativity (the curvature equations or CEs for short) that are strikingly similar to the Maxwell equations of electrodynamics. This paper considers whether Mother Nature may have used the same basic pattern for her laws of gravitation and electrodynamics, in which case the CEs might be viewed as the field equations of gravitation in place of Einstein's equation. This is not a new theory of gravitation (because the curvature equations are derivable from Einstein's equation), but rather is a mild reinterpretation of general relativity that solves the vacuum-energy problem and the dark-energy problem of cosmology. The results of this paper allow one to understand how the effective energy density of the observed cosmological constant can be so vastly smaller than estimates of the vacuum energy of quantum fields and why the vacuum energy of quantum fields does not contribute as a source of curvature.