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Quantum Cosmology - The Supersymmetric Perspective - Vol. 1 pp 251–258Cite as

Obstacles and Results: From QC to SQC

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Part of the book series: Lecture Notes in Physics ((LNP,volume 803))

Abstract

Some of the research routes in supersymmetric quantum cosmology (SQC) are imported from the objectives and subsequent results within purely bosonic quantum cosmology (QC). More precisely, the overall aim for SQC has been (and still is) to employ a more fundamental framework, richer both in content as well as assumptions, where the structure of purely bosonic quantum cosmology fits consistently as a limiting situation. SQC will constitute a vaster, more adequate, and more elegant perspective for the very early universe. Let us point here to the ‘essentials’ in the QC programme, then to the relevant features of SUGRA. Afterwards we summarize the progress subsequently achieved in SQC.

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Notes

  1. 1.

    Technically speaking, it all depends on the chosen complex contour where the integration is implemented.

  2. 2.

    Could it be that SUSY would be such a principle?

  3. 3.

    This means the necessary initial conditions for inflation must be implied by the boundary condition for the wave function of the universe.

  4. 4.

    See the landscape problem within (quantum) string cosmology [15].

References

  1. P.D. D'Eath: Supersymmetric Quantum Cosmology. Cambridge University Press, Cambridge, (1996) p. 252

    Book  Google Scholar 

  2. J.J. Halliwell: Introductory lectures on quantum cosmology. To appear in Proc. of Jerusalem Winter School on Quantum Cosmology and Baby Universes, Jerusalem, Israel, 27 December 1989–4 January 1990

    Google Scholar 

  3. J.B. Hartle: Quantum cosmology. In New Haven 1985, Proceedings, High Energy Physics, Vol. 2 (1985) pp. 471–566

    Google Scholar 

  4. S.W. Hawking: Lectures on quantum cosmology. In De Vega, H.J. and Sanchez, N. (Eds.), Field Theory, Quantum Gravity and Strings. Cambridge University Press, Cambridge (1986) pp. 1–45

    Chapter  Google Scholar 

  5. C. Kiefer. Quantum Gravity, 2nd edn., International Series of Monographs on Physics 136, Clarendon Press, Oxford (2007)

    Google Scholar 

  6. D.N. Page: Lectures on quantum cosmology. In Proceedings of Banff Summer Institute on Gravitation, Banff, Canada, 12–15 August 1990, Mann, R.B. et al. (Eds.), World Scientific, Singapore (1991)

    Google Scholar 

  7. J.B. Hartle: Quantum cosmology. Problems for the 21st century, gr-qc/9701022 (1997)

    Google Scholar 

  8. J.B. Hartle: The state of the universe, gr-qc/0209046 (2002)

    Google Scholar 

  9. C. Kiefer: Quantum gravity. A general introduction. Lect. Notes Phys. 631, 3–13 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  10. C. Kiefer: Conceptual issues in quantum cosmology. Lect. Notes Phys. 541, 158–187 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  11. J.B. Hartle and S.W. Hawking: Wave function of the universe. Phys. Rev. D 28, 2960–2975 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  12. A. Ashtekar: Lectures on Nonperturbative Canonical Gravity. Advanced Series in Astrophysics and Cosmology 6, World Scientific, Singapore (1991) p. 334

    Google Scholar 

  13. R. Gambini and J. Pullin: Loops, Knots, Gauge Theories and Quantum Gravity. Cambridge University Press, Cambridge (1996)

    Book  Google Scholar 

  14. C. Rovelli: Quantum Gravity. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  15. M. Bouhmadi-Lopez and P.V. Moniz: Quantisation of parameters and the string landscape problem, hep-th/0612149 (2006)

    Google Scholar 

  16. M.P. Ryan and L.C. Shepley: Homogeneous Relativistic Cosmologies. Princeton Series in Physics, Princeton University Press, Princeton, NJ (1975)

    Google Scholar 

  17. P. D'Eath: What local supersymmetry can do for quantum cosmology. Prepared for Workshop on Conference on the Future of Theoretical Physics and Cosmology in Honor of Steven Hawking's 60th Birthday, Cambridge, England, 7–10 January 2002

    Google Scholar 

  18. K.V. Kuchar and M.P. Ryan: Is minisuperspace quantization valid? Taub in mixmaster. Phys. Rev. D 40, 3982–3996 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  19. K.V. Kuchar and M.P. Ryan Jr.: Can minisuperspace quantization be justified? NSF-ITP-86–78 (1986)

    Google Scholar 

  20. S. Sinha and B.L. Hu: Validity of the minisuperspace approximation. An example from interacting quantum field theory. Phys. Rev. D 44, 1028–1037 (1991)

    Article  ADS  Google Scholar 

  21. S. Deser and B. Zumino: Consistent supergravity. Phys. Lett. B 62, 335 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  22. S. Ferrara, J. Scherk, and B. Zumino: Algebraic properties of extended supergravity theories. Nucl. Phys. B 121, 393 (1977)

    Google Scholar 

  23. S. Ferrara and P. Van Nieuwenhuizen: Consistent supergravity with complex spin 3/2 gauge fields. Phys. Rev. Lett. 37, 1669 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  24. D.Z. Freedman and P. Van Nieuwenhuizen: Properties of supergravity theory. Phys. Rev. D 14, 912 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  25. D.Z. Freedman, P. Van Nieuwenhuizen, and S. Ferrara: Progress toward a theory of supergravity. Phys. Rev. D 13, 3214–3218 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  26. P. Van Nieuwenhuizen: Supergravity. Phys. Rep. 68, 189–398 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  27. S. Deser, J.H. Kay, and K.S. Stelle: Hamiltonian formulation of supergravity. Phys. Rev. D 16, 2448 (1977)

    Article  ADS  Google Scholar 

  28. E.S. Fradkin and T.E. Fradkina: Quantization of relativistic systems with boson and fermion first and second class constraints. Phys. Lett. B 72, 343 (1978)

    Article  ADS  Google Scholar 

  29. E.S. Fradkin and M.A. Vasiliev: Hamiltonian formalism, quantization and S matrix for supergravity. Phys. Lett. B 72, 70 (1977)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. M. Pilati: The canonical formulation of supergravity. Nucl. Phys. B 132, 138 (1978)

    MathSciNet  Google Scholar 

  31. R. Tabensky and C. Teitelboim: The square root of general relativity. Phys. Lett. B 69, 453 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  32. 4C. Teitelboim: Supergravity and square roots of constraints. Phys. Rev. Lett. 38, 1106–1110 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  33. C. Teitelboim: Surface integrals as symmetry generators in supergravity theory. Phys. Lett. B 69, 240–244 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  34. C. Kiefer, T. Luck, and P. Moniz: The semiclassical approximation to supersymmetric quantum gravity. Phys. Rev. D 72, 045006 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  35. S.M. Carroll, D.Z. Freedman, M.E. Ortiz, and D.N. Page: Physical states in canonically quantized supergravity. Nucl. Phys. B 423, 661–687 (1994)

    MathSciNet  MATH  Google Scholar 

  36. A. Csordas and R. Graham: Exact quantum state for N = 1 supergravity. Phys. Rev. D 52, 6656–6659 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  37. P.D. D'Eath: The canonical quantization of supergravity. Phys. Rev. D 29, 2199 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  38. P.V. Moniz: Supersymmetric quantum cosmology. Shaken not stirred. Int. J. Mod. Phys. A 11, 4321–4382 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. L.J. Alty, P.D. D'Eath, and H.F. Dowker: Quantum wormhole states and local supersymmetry. Phys. Rev. D 46, 4402–4412 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  40. P.D. D'Eath and D.I. Hughes: Supersymmetric minisuperspace. Phys. Lett. B 214, 498–502 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  41. P.D. D'Eath and D.I. Hughes: Minisuperspace with local supersymmetry. Nucl. Phys. B 378, 381–409 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  42. P. Moniz: FRW minisuperspace with local N = 4 supersymmetry and self-interacting scalar field. Ann. Phys. 12, 174–198 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  43. S.W. Hawking and D.N. Page: The spectrum of wormholes. Phys. Rev. D 42, 2655–2663 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  44. J. Bene and R. Graham: Supersymmetric homogeneous quantum cosmologies coupled to a scalar field. Phys. Rev. D 49, 799–815 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  45. R. Graham: Supersymmetric Bianchi type IX cosmology. Phys. Rev. Lett. 67, 1381–1383 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. R. Graham: Supersymmetric general Bianchi type IX cosmology with a cosmological term. Phys. Lett. B 277, 393–397 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  47. R. Graham and J. Bene: Supersymmetric Bianchi type IX cosmology with a scalar field. Phys. Lett. B 302, 183–188 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  48. R. Graham and H. Luckock: The Hartle–Hawking state for the Bianchi IX model in supergravity. Phys. Rev. D 49, 4981–4984 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  49. A.D.Y. Cheng, P.D. D'Eath, and P.R.L.V. Moniz: Quantization of the Bianchi type IX model in supergravity with a cosmological constant. Phys. Rev. D 49, 5246–5251 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  50. A.D.Y. Cheng, P.D. D'Eath, and P.R.L.V. Moniz: Quantization of Bianchi models in N = 1 supergravity with a cosmological constant. Grav. Cosmol. 1, 12–21 (1995)

    ADS  MATH  Google Scholar 

  51. A. Csordas and R. Graham: Supersymmetric minisuperspace with nonvanishing fermion number. Phys. Rev. Lett. 74, 4129–4132 (1995)

    Article  ADS  Google Scholar 

  52. A. Csordas and R. Graham: Hartle–Hawking state in supersymmetric minisuperspace. Phys. Lett. B 373, 51–55 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  53. P.D. D'Eath: Quantization of the Bianchi IX model in supergravity. Phys. Rev. D 48, 713–718 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  54. P.D. D'Eath, S.W. Hawking, and O. Obregon: Supersymmetric Bianchi models and the square root of the Wheeler–DeWitt equation. Phys. Lett. B 300, 44–48 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  55. P.D. D'Eath: Quantization of the supersymmetric Bianchi I model with a cosmological constant. Phys. Lett. B 320, 12–15 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  56. A. Csordas and R. Graham: Nontrivial fermion states in supersymmetric minisuperspace, gr-qc/9503054 (1994)

    Google Scholar 

  57. R. Graham and A. Csordas: Quantum states on supersymmetric minisuperspace with a cosmological constant. Phys. Rev. D 52, 5653–5658 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  58. A.D.Y. Cheng and P.D. D'Eath: Diagonal quantum Bianchi type IX models in N = 1 supergravity. Class. Quant. Grav. 13, 3151–3162 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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  1. Depto. Fisica, Universidade da Beira Interior, Rua Marquês d’Avila e, Bolama, 6200-307, Covilhã, Portugal

    Paulo Vargas Moniz

  2. CENTRA-IST, Lisboa, Portugal

    Paulo Vargas Moniz

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Moniz, P.V. (2010). Obstacles and Results: From QC to SQC. In: Quantum Cosmology - The Supersymmetric Perspective - Vol. 1. Lecture Notes in Physics, vol 803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11575-2_7

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