On the nature of the Newton's gravitational constant and the possible quantum-field theory of gravitation

TL;DR

This paper explores the potential quantum-field theoretical nature of gravity by drawing parallels between the Newtonian gravitational constant and the Fermi constant, proposing a model where gravity is mediated by massive tensor bosons resulting from spontaneous symmetry breaking.

Contribution

It introduces a novel hypothesis that gravitational interactions may involve massive tensor bosons, similar to weak force mediators, arising from gauge symmetry breaking in a quantum-field framework.

Findings

Suggests a similarity between weak and gravitational forces based on dimensional analysis.

Proposes a mechanism for graviton mass generation via spontaneous symmetry breaking.

Lays groundwork for a quantum-field theory of gravitation involving tensor bosons.

Abstract

On the basis of the coincidence of the physical dimensions (in natural units $\hbar = c = 1$) of the Newton's gravitational constant $G_{N} $ and the phenomenological Fermi constant $G_{F} $ for weak interaction, it is suggested that there is a certain similarity between weak forces, which are caused by the exchange of massive intermediate vector bosons with spin $S=1$, and "superweak" gravitational forces that can be caused by the exchange of "supermassive" hypothetical tensor bosons with spin $S=2$. By analogy with how the masses of intermediate bosons in the theory of electroweak interaction arise as a result of spontaneous breaking of the gauge symmetry of the electromagnetic field due to its interaction with the nonlinear scalar Higgs field, the masses of hypothetical tensor bosons carrying gravitational interaction can also arise as a result of spontaneous breaking of gauge symmetry of the massless gravitons when they interact with a fundamental nonlinear scalar field in a flat 4-dimensional space-time.