General Relativity and Gravitation

, Volume 40, Issue 8, pp 1663–1681 | Cite as

Perfect fluid quantum Universe in the presence of negative cosmological constant

  • P. Pedram
  • M. Mirzaei
  • S. Jalalzadeh
  • S. S. Gousheh
Research Article


We present perfect fluid Friedmann–Robertson–Walker quantum cosmological models in the presence of negative cosmological constant. In this work the Schutz’s variational formalism is applied for radiation, dust, cosmic string, and domain wall dominated Universes with positive, negative, and zero constant spatial curvature. In this approach the notion of time can be recovered. These give rise to Wheeler–DeWitt equations for the scale factor. We find their eigenvalues and eigenfunctions by using Spectral Method. After that, we use the eigenfunctions in order to construct wave packets for each case and evaluate the time-dependent expectation value of the scale factors, which are found to oscillate between finite maximum and minimum values. Since the expectation values of the scale factors never tends to the singular point, we have an initial indication that these models may not have singularities at the quantum level.


Quantum cosmology Wheeler–DeWitt equation Spectral method 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • P. Pedram
    • 1
  • M. Mirzaei
    • 1
  • S. Jalalzadeh
    • 1
  • S. S. Gousheh
    • 1
  1. 1.Department of PhysicsShahid Beheshti UniversityEvin, TehranIran

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