  It is shown that nonlinear terms in equations of gravitons on the background
of curved space-time of the expanding Universe can solve the problem of the
negative square of the effective mass formally arising in linear approximation
for gravitons. Similar to well known spontaneous breaking of symmetry in
Goldstone model one must take another vacuum so that nonzero vacuum expectation
value of the quantized graviton field leads to change of spectrum for
gravitons. There appears two graviton fields, one with the positive mass,
another with the zero mass. Energy density and the density of particles created
by gravitation of the expanding Universe are calculated for some special cases
of the scale factor. Numerical of result are obtained for the dust universe
case.
