On calculation of the cosmological parameters in exact models of inflation

S.V. Chervon and I.V. Fomin1

Abstract

We discuss a method of calculating the key cosmological parameters on the basis of a selected scale factor by using exact solutions of the background equations. We specify the formulas for calculating the power spectrum, the spectral indices and their ratios, and the ratio of squared amplitudes of scalar and tensor perturbations. We obtain, for the first time, expressions for the basic cosmological parameters in terms of the scalar factor value at the instant of crossing the cosmological horizon. In this case, the cosmological parameters are calculated for a wide class of exact models. They are compared with their analogs derived in the slow-rolling approximation.

References

  1. A. A. Starobinsky, Phys. Lett. B 918 24 (1980); A. H. Guth, Phys. Rev. D 23 347 (1981); A. D. Linde, Phys. Lett. B 108 389 (1982); A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48 1220 (1982).
  2. V. N. Lukash, Uspekhi Fiz. Nauk 176, 113 (2006).
  3. A. R. Liddle and D. H. Lyth, Phys. Rep. 231, 1 (1993).
  4. S. V. Chervon, Gen. Rel. Grav. 36 1547 (2004).
  5. A. Riotto, Inflation and the Theory of Cosmological Perturbations, hep-ph/0210162.
  6. S. V. Chervon, M. Novello and R. Triay, Grav. & Cosmol. 11 329 (2005).
  7. S. V. Chervon, Exact inflation and the key cosmological parameters. In: Proc. of the Russian School and International Conference on Gravitation, Cosmology and Relativistic Astrophysics GRACOS-2007, 09-16 September 2007, TGGPU, Kazan-Yalchik, 2007, pp. 174-178; S. V. Chervon, Exact inflation and cosmological parameters, Issledovano v Rossii (electronic journal), No. 100, pp. 1035-1040 (2007); http://zhurnal.ape.relarn.ru/articles/2007/100.pdf
  8. S. V. Chervon, Nonlinear Fields in the Theory of Gravitation and Cosmology (Middle-Volga Scientific Center, Ulyanovsk State University, 1997).
  9. S. V. Chervon, V. M. Zhuravlev, and V. K. Shchigolev, Phys. Lett. B 398 269 (1997).
  10. G. F. R. Ellis and M. S. Madsen, Class. Quant. Grav. 8 667 (1991).
  11. J. D. Barrow, Phys. Rev. D 49 3055 (1994).
  12. R. Maartens, D. R. Taylor and N. Roussos, Phys. Rev. D 52 3358 (1995).
  13. V. M. Zhuravlev and S. V. Chervon, JETP 118, 259 (2000).
  14. A. H. Guth, Inflation, astro-ph/0404546.
  15. E. D. Stewart, The spectrum of density perturbations produced during inflation to leading order in a general slow-roll approximation, astro-ph/0110322.
  16. P. Binetruy and M. K. Gaillard. Phys. Rev. D 34 3069 (1986).
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