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

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.