Spontaneous symmetry breaking for long-wave gravitons in the early Universe

A.A. Grib and V.Yu. Dorofeev1

Abstract

It is shown that nonlinear terms in the equations for gravitons in the background of curved space-time of the expanding Universe can solve the problem of the negative effective mass squared, formally arising in the linear approximation for gravitons. Similarly to the well-known spontaneous symmetry breaking in the Goldstone model, one must take another vacuum, so that a nonzero vacuum expectation value of the quantized graviton field leads to a change in the graviton spectrum. There appear two graviton fields, one with positive mass, another with zero mass. The 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 results are obtained for the case of a dust universe.

References

  1. A. A. Grib, S. G. Mamayev, and V. M. Mostepanenko, Vacuum Quantum Effects in Strong Fields (Friedmann Lab Publ., St. Petersburg, 1994).
  2. L. P. Grishuk, Relic Gravitational Waves and Cosmology, Uspekhi Fiz. Nauk 175, 12 (2005).
  3. E. M. Lifshits, Gravitational Stabilities of the Expanding World, Zh. Eksp. Teor. Fiz. 16, 587 (1946).
  4. L. D. Landau and E. M. Lifshits, Field theory (Nauka, Moscow, 1973).
  5. L. P. Grishchuk, Amplification of Gravitational Waves in the Isotropic World, Zh. Eksp. Teor. Fiz. 67, 825 (1974).
  6. L. H. Ford and L. P. Parker, Quantized Gravitational Wave Perturbations in Robertson-Walker Universes, Phys. Rev. D, 16, 1601 (1977).
  7. V. Sahni, Energy Density of Relic Gravity Waves from Inflation, Phys. Rev. D 42, 453 (1990).
  8. A. A. Starobinsky, Spectrum of Relic Gravitational Radiation and the Initial State of the Universe, Pis'ma v Zh. Eksp. Teor. Fiz. 30, 719 (1979) [Sov. Phys. - JETP Lett. 30, 682 (1979)].
  9. S. Weinberg, Gravitation and Cosmology (Platon, Moscow, 2000).
  10. V. Yu. Dorofeev, Expansion of Einstein Equations of Backgraund Gravitational Field, in: Quantum Theory and Cosmology (Friedmann Lab. Publ., St. Petersburg, 2009).
For more information about this paper please visit Springer's Home Page of this paper.



Back to The Contents Page