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Quantum Cosmology

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Part of the Springer Theses book series (Springer Theses)

Abstract

In this chapter we will investigate the cosmos as a whole. First, we will try to approach the fundamental questions about the cosmos by resorting to various ideas and conceptional questions in order to understand the environment we live in. Then, we will investigate the tunnelling scenario in the framework of quantum cosmology. Finally, we will apply the results of the previous chapter to derive initial conditions for inflation.

Keywords

Quantum Correlation Reduce Density Matrix Quantum Cosmology Cosmological Horizon Lapse Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Antoniadis, I., Mazur, P.O., Mottola, E.: Scaling behavior of quantum four-geometries. Phys. Lett. B 323, 284 (1994)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Antoniadis, I., Mottola, E.: Four-dimensional quantum gravity in the conformal sector. Phys. Rev. D 45, 2013 (1992)MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Asaka, T., Blanchet, S., Shaposhnikov, M.: The \(\nu \)MSM, dark matter and neutrino masses. Phys. Lett. B 631, 151 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    Asaka, T., Shaposhnikov, M.: The \(\nu \)MSM, dark matter and baryon asymmetry of the universe. Phys. Lett. B 620, 17 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    Barvinsky, A.O.: Unitarity approach to quantum cosmology. Phys. Rep. 230, 237 (1993)MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Barvinsky, A.O.: Reduction methods for functional determinants in quantum gravity and cosmology. Phys. Rev. D 50, 5115 (1994)MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Barvinsky, A.O.: Why there is something rather than nothing: cosmological constant from summing over everything in Lorentzian quantum gravity. Phys. Rev. Lett. 99, 071301 (2007)MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Barvinsky, A.O., Deffayet, C.: Anomaly driven cosmology: big boost scenario and AdS/CFT correspondence. J. Cosmol. Astropart. Phys. 05, 020 (2008)Google Scholar
  9. 9.
    Barvinsky, A.O., Kamenshchik, A.Yu.: 1-loop quantum cosmology: the normalizability of the Hartle-Hawking wave function and the probability of inflation. Class. Quantum Grav. 7, L181 (1990)Google Scholar
  10. 10.
    Barvinsky, A.O., Kamenshchik, A.Yu.: Quantum scale of inflation and particle physics of the early universe. Phys. Lett. B 332, 270 (1994)Google Scholar
  11. 11.
    Barvinsky, A.O., Kamenshchik, A.Yu.: Effective equations of motion and initial conditions for inflation in quantum cosmology. Nucl. Phys. B 532, 339 (1998)Google Scholar
  12. 12.
    Barvinsky, A.O., Kamenshchik, A.Yu.: Cosmological landscape from nothing: some like it hot. J. Cosmol. Astropart. Phys. 09, 014 (2006)Google Scholar
  13. 13.
    Barvinsky, A.O., Kamenshchik, A.Yu.: Thermodynamics via creation from nothing: Limiting the cosmological constant landscape. Phys. Rev. D 74, 121502 (2006)Google Scholar
  14. 14.
    Barvinsky, A.O., Kamenshchik, A.Yu.: Effective action and decoherence by fermions in quantum cosmology. Nucl. Phys. B 552, 420 (1999)Google Scholar
  15. 15.
    Barvinsky, A.O., Kamenshchik, A.Yu.: Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field. J. Cosmol. Astropart. Phys. 12, 003 (2009)Google Scholar
  16. 16.
    Barvinsky, A.O., Kamenshchik, A.Yu.: Higgs boson, renormalization group, and naturalness in cosmology. Eur. Phys. J. C. 72, 2219 (2012)Google Scholar
  17. 17.
    Barvinsky, A.O., Kamenshchik, A.Yu.: Inflation scenario via the Standard Model Higgs boson and LHC. J. Cosmol. Astropart. Phys. 11, 021 (2008)Google Scholar
  18. 18.
    Barvinsky, A.O., Nesterov, D.V.: Effective equations in quantum cosmology. Nucl. Phys. B 608, 333 (2001)MathSciNetADSCrossRefzbMATHGoogle Scholar
  19. 19.
    Bell, J.S.: On the Einstein-Podolsky-Rosen paradox. Physics 1, 195 (1964)Google Scholar
  20. 20.
    Bezrukov, F., Shaposhnikov, M.: Standard model Higgs boson mass from inflation: two loop analysis. J. High Energy Phys. 07, 089 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    Bezrukov, F.L., Magnin, A., Shaposhnikov, M.: Standard Model Higgs boson mass from inflation. Phys. Lett. B 675, 88 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    Bohr, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 48, 696 (1935)ADSCrossRefzbMATHGoogle Scholar
  23. 23.
    Brezger, B., Hackmüller, L., Uttenthaler, S., Petschinka, J., Arndt, M., Zeilinger, A.: Matter-wave interferometer for large molecules. Phys. Rev. Lett. 88, 100404 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    Clark, T.E., Liu, B., Love, S.T., ter Veldhuis, T.: Standard model Higgs boson-inflaton and dark matter. Phys. Rev. D 80, 075019 (2009)ADSCrossRefGoogle Scholar
  25. 25.
    Coleman, S.: Aspects of Symmetry. Cambridge University Press, Cambridge (1985)CrossRefzbMATHGoogle Scholar
  26. 26.
    De Simone, A., Hertzberg, M.P., Wilczek, F.: Running inflation in the standard model. Phys. Lett. B 678, 1 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    DeWitt, B.S.: Quantum theory of gravity. I canonical theory. Phys. Rev. 160, 1113 (1967)ADSCrossRefzbMATHGoogle Scholar
  28. 28.
    DeWitt, B.S., Graham, N.: The Many-Worlds Interpretation of Quantum Mechanics. Princeton University Press, Princeton (1973)Google Scholar
  29. 29.
    Dirac, P.A.M.: Lectures on Quantum Mechanics, 2nd edn. Yeshiva University, New York, Belfer Graduate School of Science (1964)Google Scholar
  30. 30.
    Espinosa, J.R., Giudice, G.F., Riotto, A.: Cosmological implications of the Higgs mass measurement. J. Cosmol. Astropart. Phys. 05, 002 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    Everett, H.: “Relative State” formulation of quantum mechanics. Rev. Mod. Phys. 29, 454 (1957)MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    Fischetti, M. V., Hartle, J. B., Hu, B. L. Quantum effects in the early universe. I. Influence of trace anomalies on homogeneous, isotropic, classical geometries. Phys. Rev. D 20, 1757 (1979)Google Scholar
  33. 33.
    Fradkin, E.S., Tseytlin, A.A.: Conformal anomaly in Weyl theory and anomaly free superconformal theories. Phys. Lett. B 134, 187 (1984)MathSciNetADSCrossRefzbMATHGoogle Scholar
  34. 34.
    Hackmüller, L., Hornberger, K., Brezger, B., Zeilinger, A., Arndt, M.: Decoherence of matter waves by thermal emission of radiation. Nature 427, 711 (2004)ADSCrossRefGoogle Scholar
  35. 35.
    Halliwell, J. J., Louko, J.: Steepest-descent contours in the path-integral approach to quantum cosmology. III. A general method with applications to anisotropic minisuperspace models. Phys. Rev. D 42, 3997 (1990)Google Scholar
  36. 36.
    Hartle, J.B., Hawking, S.W.: Wave function of the Universe. Phys. Rev. D 28, 2960 (1983)MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    Hawking, S.W.: The boundary condition of the universe. Pontificia Acad. Scientarium Scr. Varia 48, 563 (1982)Google Scholar
  38. 38.
    Hawking, S.W.: The quantum state of the universe. Nucl. Phys. B 239, 257 (1984)MathSciNetADSCrossRefGoogle Scholar
  39. 39.
    Kiefer, C.: On the meaning of path integrals in quantum cosmology. Ann. Phys. (NY) 207, 53 (1991)MathSciNetADSCrossRefzbMATHGoogle Scholar
  40. 40.
    Kiefer, C.: Decoherence in quantum electrodynamics and quantum gravity. Phys. Rev. D 46, 1658 (1992)ADSCrossRefGoogle Scholar
  41. 41.
    Kiefer, C.: Semiclassical gravity and the problem of time. http://arxiv.org/abs/gr-qc/9405039 (1993). Accessed 11 January 2012 (6 pages)
  42. 42.
    Kiefer, C.: Conceptual issues in quantum cosmology. Lect. Notes Phys. 541, 158 (2000)MathSciNetADSCrossRefGoogle Scholar
  43. 43.
    Kiefer, C.: Quantum Gravity, 2nd edn. Oxford University Press, Oxford (2007)CrossRefzbMATHGoogle Scholar
  44. 44.
    Kiefer, C., Lohmar, I., Polarski, D., Starobinsky, A.A.: Origin of classical structure in the Universe. J. Phys. Conf. Ser. 67, 012023 (2007)ADSCrossRefGoogle Scholar
  45. 45.
    Kiefer, C., Singh, T.P.: Quantum gravitational corrections to the functional Schrödinger equation. Phys. Rev. D 44, 1067 (1991)MathSciNetADSCrossRefGoogle Scholar
  46. 46.
    Linde, A.D.: Quantum creation of an inflationary universe. Sov. Phys. JETP 60, 211 (1984)Google Scholar
  47. 47.
    Linde, A.D.: Quantum creation of the inflationary universe. Lett. Nuovo Cimento 39, 401 (1984)ADSCrossRefGoogle Scholar
  48. 48.
    Linde, A.D.: Eternal chaotic inflation. Mod. Phys. Lett. A 1, 81 (1986)ADSCrossRefGoogle Scholar
  49. 49.
    Marolf, D.: Resource letter NSST-1: the nature and status of string theory. Am. J. Phys. 72, 730 (2004)MathSciNetADSCrossRefzbMATHGoogle Scholar
  50. 50.
    Perlmutter, S., et al., Supernova Cosmology Project.: Measurements of \(\Omega \) and \(\Lambda \) from 42 high-redshift supernovae. Astrophys. J. 517, 565 (1999)Google Scholar
  51. 51.
    Popper, K.: Logik der Forschung. Springer, Vienna (1935)CrossRefGoogle Scholar
  52. 52.
    Riegert, R.J.: A nonlocal action for the trace anomaly. Phys. Lett. B 134, 56 (1984)MathSciNetADSCrossRefzbMATHGoogle Scholar
  53. 53.
    Rubakov, V.A.: Particle creation in a tunneling universe. JETP Lett. 39, 107 (1984)ADSGoogle Scholar
  54. 54.
    Schlosshauer, M.A.: Decoherence and the Quantum-To-Classical Transition. Springer, Berlin (2007)Google Scholar
  55. 55.
    Schmitt-Manderbach, T., et al.: Experimental demonstration of free-space decoy-state quantum key distribution over 144 km. Phys. Rev. Lett. 98, 010504 (2007)Google Scholar
  56. 56.
    Schrödinger, E.: Die gegenwärtige Situation in der Quantenmechanik. Naturwiss 23, 807 (1935)ADSCrossRefGoogle Scholar
  57. 57.
    Shaposhnikov, M., Zenhausern, D.: Quantum scale invariance, cosmological constant and hierarchy problem. Phys. Lett. B 671, 162 (2009)MathSciNetADSCrossRefGoogle Scholar
  58. 58.
    Sher, M.: Electroweak Higgs potentials and vacuum stability. Phys. Rep. 179, 273 (1989)ADSCrossRefGoogle Scholar
  59. 59.
    Starobinsky, A.A.: A new type of isotropic cosmological models without singularity. Phys. Lett. B 91, 99 (1980)ADSCrossRefGoogle Scholar
  60. 60.
    Susskind, L.: The anthropic landscape of string theory. http://arxiv.org/abs/hep-th/0302219 (2003). Accessed 11 January 2012 (22 pages)
  61. 61.
    Tegmark, M.: The multiverse hierarchy. http://arxiv.org/abs/0905.1283 (2007). Accessed 11 January 2012 (15 pages)
  62. 62.
    Vachaspati, T., Vilenkin, A.: Uniqueness of the tunneling wave function of the universe. Phys. Rev. D 37, 898 (1988)MathSciNetADSCrossRefGoogle Scholar
  63. 63.
    Vilenkin, A.: Creation of universes from nothing. Phys. Lett. B 117, 25 (1982)MathSciNetADSCrossRefGoogle Scholar
  64. 64.
    Vilenkin, A.: Quantum creation of universes. Phys. Rev. D 30, 509 (1984)MathSciNetADSCrossRefGoogle Scholar
  65. 65.
    Vilenkin, A.: Quantum cosmology and the initial state of the universe. Phys. Rev. D 37, 888 (1988)MathSciNetADSCrossRefGoogle Scholar
  66. 66.
    Vilenkin, A.: Approaches to quantum cosmology. Phys. Rev. D 50, 2581 (1994)MathSciNetADSCrossRefGoogle Scholar
  67. 67.
    Vilenkin, A.: The quantum cosmology debate. http://arxiv.org/abs/gr-qc/9812027 (1998). Accessed 11 January 2012 (9 pages)
  68. 68.
    Vilenkin, A.: The Wave function discord. Phys. Rev. D 58, 067301 (1998)MathSciNetADSCrossRefGoogle Scholar
  69. 69.
    von Neumann, J.: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1932)zbMATHGoogle Scholar
  70. 70.
    Wheeler, J.A.: Superspace and the nature of quantum geometrodynamics. In: DeWitt, C.M., Wheeler, J.A. (eds.) Battelle Rencontres, pp. 242–307. Benjamin, New York (1968)Google Scholar
  71. 71.
    Wigner, E.P.: Remarks on the mind-body question. In: Good, I.J. (ed.) The Scientist Speculates: An Anthology of Partly-Baked Ideas, pp. 284–302. Heinemann, London (1961)Google Scholar
  72. 72.
    Zeh, H.D.: On the interpretation of measurement in quantum theory. Found. Phys. 1, 69 (1970)ADSCrossRefGoogle Scholar
  73. 73.
    Zeldovich, Y.B., Starobinsky, A.A.: Quantum creation of a universe in a nontrivial topology. Sov. Astron. Lett. 10, 135 (1984)ADSGoogle Scholar
  74. 74.
    Zurek, W. H.: Decoherence and the transition from quantum to classical. Phys. Today 44N10, 36 (1991)Google Scholar
  75. 75.
    Zurek, W.H.: Probabilities from entanglement, Born’s rule \(p_{k}=|\psi _{k}|^2\) from envariance. Phys. Rev. A 71, 052105 (2005)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamUK

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