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

TL;DR

The paper demonstrates that nonlinear effects in gravitons within an expanding Universe can resolve issues with negative effective mass squared, leading to spontaneous symmetry breaking and a modified graviton spectrum.

Contribution

It introduces a nonlinear approach to graviton equations that results in spontaneous symmetry breaking, altering the graviton spectrum in the early Universe.

Findings

Nonlinear terms resolve negative mass squared problem.

Two graviton fields with different masses emerge.

Numerical results provided for dust universe case.

Abstract

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.