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It is shown that nonlinear terms in equations of gravitons on the backgroundof curved space-time of the expanding Universe can solve the problem of thenegative square of the effective mass formally arising in linear approximationfor gravitons. Similar to well known spontaneous breaking of symmetry inGoldstone model one must take another vacuum so that nonzero vacuum expectationvalue of the quantized graviton field leads to change of spectrum forgravitons. There appears two graviton fields, one with the positive mass,another with the zero mass. Energy density and the density of particles createdby gravitation of the expanding Universe are calculated for some special casesof the scale factor. Numerical of result are obtained for the dust universecase.

Spontaneous breaking of symmetry of the gravitons of the long wave spectrum in the early Universe