Physics of Particles and Nuclei

, Volume 49, Issue 4, pp 514–519 | Cite as

Third Quantization and Emergence of the Quasiclassical Wave Function of the Universe

  • P. Ivanov
  • S. V. Chernov


Quantized solutions of the Wheeler–DeWitt (WDW) equation describing a closed Friedmann–Robertson–Walker universe with a \(\Lambda \) term and a set of massless scalar fields are studied. It is shown that when \(\Lambda \ll 1\) units and the standard in-vacuum state is considered, the wave function of the universe \(\Psi \) behaves as a random quasiclassical field at rather large a, namely, \(1 \ll a \ll {{e}^{{\frac{2}{{3\Lambda }}}}}\) [1].



The work was supported by Grant NSh-6595.2016.2 of the President of the Russian Federation for Support of Leading Scientific Schools.


  1. 1.
    P. Ivanov and S. V. Chernov, “Stochastic quasiclassical wave function of the universe from the third quantization procedure,” Phys. Rev. D 92, 063507 (2015).ADSCrossRefGoogle Scholar
  2. 2.
    B. S. DeWitt, “Quantum theory of gravity. 1. The canonical of theory,” Phys. Rev. 160, 1113 (1967).ADSCrossRefMATHGoogle Scholar
  3. 3.
    C. Kiefer, Quantum Gravity, 2nd ed. (Oxford University Press, 2007).CrossRefMATHGoogle Scholar
  4. 4.
    A. Vilenkin, “Quantum creation of universes,” Phys. Rev. D 30, 509 (1984).ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    J. B. Hartle and S. W. Hawking, “Wave function of the universe,” Phys. Rev. D 28, 2960 (1983).ADSMathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Chicago University Press, 1982).CrossRefMATHGoogle Scholar
  7. 7.
    V. A. Rubakov, “On third quantization and the cosmological constant,” Phys. Lett. B 214, 503 (1988).ADSCrossRefGoogle Scholar
  8. 8.
    S. Abe, “Fluctuations around the Wheeler-DeWitt trajectories in third-quantized cosmology,” Phys. Rev. D 47, 718 (1993).ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    D. Polarski and A. A. Starobinsky, “Semiclassicality and decoherence of cosmological perturbations,” Classical Quantum Gravity 13, 377 (1996).ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Astro Space Centre, Lebedev Physical InstituteMoscowRussia

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