On particle creation and renormalization in a cosmological model with a Big Rip

Yu.V. Pavlov1


An exact solution is obtained for a massive scalar field conformally coupled with the curvature in a cosmological model with the scale factor a(t) = a0/|t|, corresponding to background matter with the equation of state p = -5eps/3. An expression for the number density of created particles is obtained, and its behavior is studied as the model approached the instant of a Big Rip. Renormalization of the energy-momentum tensor is considered, and it is shown that back reaction of the quantum effects of a conformally coupled scalar field on the space-time metric can be neglected if the field mass is much smaller than the Planck mass and if the time left to the Big Rip is greater than the Planck time.


  1. A. A. Grib, S. G. Mamayev, and V. M. Mostepanenko, Vacuum Quantum Effects in Strong Fields (Friedmann Lab. Publ., St. Petersburg, 1994).
  2. A. A. Grib and Yu. V. Pavlov, Int. J. Mod. Phys. D 11, 433 (2002); Int. J. Mod. Phys. A 17, 4435 (2002); Grav. Cosmol. 14, 1 (2008).
  3. A. A. Grib and Yu. V. Pavlov, Mod. Phys. Lett. A 23, 1151 (2008); Grav. Cosmol. 15, 44 (2009).
  4. Yu. V. Pavlov, Teor. Mat. Fiz. 126, 115 (2001) [English transl.: Theor. Math. Phys. 126, 92 (2001)].
  5. A. A. Starobinsky, Grav. Cosmol. 6, 157 (2000); R. R. Caldwell, Phys. Lett. B 545, 23 (2002).
  6. V. F. Zaitsev and A. D. Polyanin, Reference Book on Ordinary Differential Equations (Fizmatlit, MOscow, 2001, in Russian).
  7. Higher Transcendental Functions (Bateman Manuscript Project), Vol. 1. Ed. A. Erdelyi. (McGraw-Hill, New York, 1953)].
  8. Ya. B. Zel'dovich and A. A. Starobinsky, Zh. Eksp. Teor. Fiz. 61 2161 (1971); Sov. Phys. JETP 34 1159 (1972).
  9. Yu. V. Pavlov, Teor. Mat. Fiz. 138, 453 (2004) [English transl.: Theor. Math. Phys. 138, 383 (2004)].
  10. A. B. Batista, J. C. Fabris, and S. J. M. Houndjo, Grav. Cosmol. 14, 140 (2008).
  11. S. Nojiri and S. D. Odintsov, Phys. Lett. B 595, 1 (2004).
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