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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 thephenomenological Fermi constant $G_{F} $ for weak interaction, it is suggestedthat there is a certain similarity between weak forces, which are caused by theexchange 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 ofintermediate bosons in the theory of electroweak interaction arise as a resultof spontaneous breaking of the gauge symmetry of the electromagnetic field dueto its interaction with the nonlinear scalar Higgs field, the masses ofhypothetical tensor bosons carrying gravitational interaction can also arise asa result of spontaneous breaking of gauge symmetry of the massless gravitonswhen they interact with a fundamental nonlinear scalar field in a flat4-dimensional space-time.

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