  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.
