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Starobinsky model in Schrödinger description

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Abstract

In the Starobinsky inflationary model inflation is driven by quantum corrections to the vacuum Einstein equation. We reduce the Wheeler-DeWitt equation corresponding to the Starobinsky model to a Schrödinger form containing time. The Schrödinger equation is solved with a Gaussian ansatz. Using the prescription for the normalization constant of the wave function given in our previous work, we show that the Gaussian ansatz demands Hawking type initial conditions for the wave function of the universe. The wormholes induce randomness in initial states suggesting a basis for time-contained description of the Wheeler-DeWitt equation.

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References

  1. A H Guth, Phys. Rev. D23, 347 (1981)

    ADS  Google Scholar 

  2. A A Starobinsky, Phys. Lett. B91, 99 (1980)

    ADS  Google Scholar 

  3. W Boucher, G W Gibbons and G T Horewitz, Phys. Rev. D30, 2447 (1984)

    ADS  Google Scholar 

  4. M B Mijic, M S Morris and W M Suen, Suen, Phys. Rev. D34, 2934 (1986)

    ADS  Google Scholar 

  5. K Maeda, Phys. Rev. D37, 858 (1988)

    ADS  Google Scholar 

  6. A Vilenkin, Phys. Rev. D27, 2848 (1983)

    ADS  MathSciNet  Google Scholar 

  7. A Vilenkin, Phys. Rev. D32, 2511 (1985)

    ADS  MathSciNet  Google Scholar 

  8. A Vilenkin, Phys. Rev. D37, 888 (1987)

    ADS  MathSciNet  Google Scholar 

  9. S W Hawking, Nucl. Phys. B239, 257 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  10. S W Hawking and D N Page, Nucl. Phys. B264, 184 (1986)

    ADS  MathSciNet  Google Scholar 

  11. A A Starobinsky and H J Schmidt, Class. Quantum. Gravit. 4, 694 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  12. R M Wald, Phys. Rev. D28, 2118 (1983)

    ADS  MathSciNet  Google Scholar 

  13. E Mottola, Phys. Rev. D31, 754 (1985)

    ADS  MathSciNet  Google Scholar 

  14. D E Nevelli, Phys. Rev. D8, 1695 (1984)

    ADS  Google Scholar 

  15. J J Halliwell and S W Hawking, Phys. Rev. D31, 1777 (1985)

    ADS  MathSciNet  Google Scholar 

  16. C Kiefer, Class. Quantum. Gravit. 4, 1369 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  17. C Kiefer, Phys. Rev. D46, 1658 (1992); D45, 2044 (1992)

    ADS  Google Scholar 

  18. C Kiefer, in Time, temporality, Now edited by H Atmanspacher and R Buhnau (Springer, Berlin, 1997) pp 227–240

    Google Scholar 

  19. C Kiefer, D Polarski and A A Starobinsky, gr-qc/9802003

  20. S Wada, Nucl. Phys. B276, 729 (1986)

    Article  ADS  Google Scholar 

  21. K V Kuchar, in Proceedings of the fourth Canadian conference on general relativity and relativity astrophysics edited by G Kunstatter, D Vincent and J Williams (World Scientific, Singapore, 1992) pp. 211–314

    Google Scholar 

  22. E Santamato, Phys. Rev. D29, 216 (1984)

    ADS  MathSciNet  Google Scholar 

  23. E Madelung, Z. Phys. 40, 332 (1926)

    Google Scholar 

  24. D Bohm, Phys. Rev. 85, 166 (1952)

    Article  ADS  MathSciNet  Google Scholar 

  25. I Feynes, Z. Phys. 132, 81 (1952)

    Article  ADS  Google Scholar 

  26. D Kershaw, Phys. Rev. B136, 1850 (1962)

    MathSciNet  Google Scholar 

  27. E Nelson, Phys. Rev. 150, 1079 (1966)

    Article  ADS  Google Scholar 

  28. S Biswas, A Shaw, B Modak and D Biswas, Quantum gravity equation in Schrödinger form in minisuperspace description, gr-qc/9906011

  29. J Butterfield and C J Isham, gr-qc/9901024

  30. C J Isham, gr-qc/9210011

  31. S Biswas, B Modak and D Biswas, Phys. Rev. D55, 4673 (1996)

    ADS  MathSciNet  Google Scholar 

  32. I Klebanov, L Susskind and T Banks, Nucl. Phys. B317, 665 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  33. S Coleman, Nucl. Phys. B310, 643 (1988)

    Article  ADS  Google Scholar 

  34. H D Conradi and H D Zeh, Phys. Lett. A154, 321 (1991)

    ADS  Google Scholar 

  35. S Biswas, A Shaw and B Modak, General Relativity and Gravitation 31, 1015 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  36. J Z Simon, Phys. Rev. D45, 1953 (1992)

    ADS  Google Scholar 

  37. L Parker and J Z Simon, Phys. Rev. D47, 1339 (1993)

    ADS  MathSciNet  Google Scholar 

  38. S Biswas, A Shaw and B Modak, Time in Quantum Gravity, gr-qc/9906010

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Authors and Affiliations

  1. Department of Physics, University of Kalyani, 741 235, Kalyani, India

    S Biswas, A Shaw & D Biswas

  2. Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, 411 007, Pune, Ganeshkhind, India

    S Biswas

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  1. S Biswas
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  2. A Shaw
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  3. D Biswas
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Biswas, S., Shaw, A. & Biswas, D. Starobinsky model in Schrödinger description. Pramana - J Phys 53, 815–831 (1999). https://doi.org/10.1007/s12043-999-0115-7

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  • DOI: https://doi.org/10.1007/s12043-999-0115-7

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