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6
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2742613997
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Tufts University Report No. gr-qc/9507018 (unpublished
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“Predictions From Quantum Cosmology,” Tufts University Report No. gr-qc/9507018 (unpublished).
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Predictions From Quantum Cosmology
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7
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0001662157
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The principle of mediocrity is a version of the anthropic principle. For a review of the latter
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The principle of mediocrity is a version of the anthropic principle. For a review of the latter, see, e.g., B. Carter, Philos. Trans. R. Soc. London A310, 347 (1983);
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(1983)
Philos. Trans. R. Soc. London
, vol.A310
, pp. 347
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Carter, B.1
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8
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0003829101
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Clarendon, Oxford
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J. D. Barrow and F. J. Tipler, The Antropic Cosmological Principle (Clarendon, Oxford, 1986). Ideas related to the principle of mediocrity have also been discussed by Albrecht 5 and by Garcia-Bellido and Linde 6.
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(1986)
The Antropic Cosmological Principle
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Barrow, J.D.1
Tipler, F.J.2
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11
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85035218129
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More exactly, the probabilities are proportional to the volumes of the thermalization hypersurfaces which are the boundaries of the corresponding thermalized regions. For details, see Refs. 11,3
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More exactly, the probabilities are proportional to the volumes of the thermalization hypersurfaces which are the boundaries of the corresponding thermalized regions. For details, see Refs. 11,3 .
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17
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85035205916
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edited by H. J. de Vega and N. Sanchez, Lecture Notes in Physics, Springer, Heidelberg
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A. A. Starobinsky, in Field Theory, Quantum Gravity and Strings, Proceedings of the Seminar Series, Meudon and Paris, France, 1984-1985, edited by H. J. de Vega and N. Sanchez, Lecture Notes in Physics Vol. 246 (Springer, Heidelberg, 1986).
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(1986)
Field Theory, Quantum Gravity and Strings, Proceedings of the Seminar Series, Meudon and Paris, France, 1984-1985
, vol.246
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Starobinsky, A.A.1
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23
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4243844250
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For a recent review of quantum cosmology, see, e.g., the second paper in Ref. 3 . The distribution (5) for the tunneling wave function was obtained by
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For a recent review of quantum cosmology, see, e.g., the second paper in Ref. 3 . The distribution (5) for the tunneling wave function was obtained by A. Vilenkin, Phys. Rev. D 30, 509 (1984).
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(1984)
Phys. Rev. D
, vol.30
, pp. 509
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Vilenkin, A.1
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24
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51249185895
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The same distribution was found using a different approach
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The same distribution was found using a different approach byA. D. Linde, Lett. Nuovo Cimento 39, 401 (1984).
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(1984)
Lett. Nuovo Cimento
, vol.39
, pp. 401
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Linde, A.D.1
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25
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33744514237
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The Euclidean approach of
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The Euclidean approach of J. B. Hartle and S. W. Hawking [Phys. Rev. D 28, 2960 (1983)] gives a drastically different probability distribution.
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(1983)
Phys. Rev. D
, vol.28
, pp. 2960
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Hartle, J.B.1
Hawking, S.W.2
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26
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85035228229
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Omitted end note
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Omitted end note.
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28
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85035195767
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This is achieved by a generalization of the method used in 15 for the potential V(φ)=λ(formula presented) and in 14 for a particular factor ordering and time variable. The transformation into a self-adjoint form can similarly be performed for a general factor ordering (13) and time variable (10
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This is achieved by a generalization of the method used in 15 for the potential V(φ)=λ(formula presented) and in 14 for a particular factor ordering and time variable. The transformation into a self-adjoint form can similarly be performed for a general factor ordering (13) and time variable (10).
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30
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0003474751
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Cambridge University Press, Cambridge, England
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, Cambridge, England, 1992).
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(1992)
Numerical Recipes in C, 2nd ed.
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Press, W.H.1
Teukolsky, S.A.2
Vetterling, W.T.3
Flannery, B.P.4
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31
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85035196729
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A related observation was made by Linde and Mezhlumian 10 who noted sensitive dependence of the results on the boundary condition they imposed at the Planck scale
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A related observation was made by Linde and Mezhlumian 10 who noted sensitive dependence of the results on the boundary condition they imposed at the Planck scale.
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32
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85035205153
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Omitted end note
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Omitted end note.
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34
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26744434931
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The case of thermalization to continuous distribution of vacua was considered, by a different approach
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The case of thermalization to continuous distribution of vacua was considered, by a different approach, inJ. Garcia-Bellido, A. D. Linde and D. A. Linde, Phys. Rev. D 50, 730 (1994);
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(1994)
Phys. Rev. D
, vol.50
, pp. 730
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Garcia-Bellido, J.1
Linde, A.D.2
Linde, D.A.3
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37
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85035224848
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Omitted end note
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Omitted end note.
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38
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85035234791
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Note also that if we accept Eq. (87) as the genuine uncertainty of the model, then values of &γtilde;/γ with a relative deviation of order (formula presented) from the maximum should still be assigned nonzero probabilities
-
Note also that if we accept Eq. (87) as the genuine uncertainty of the model, then values of &γtilde;/γ with a relative deviation of order (formula presented) from the maximum should still be assigned nonzero probabilities.
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39
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33748878350
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Proceedings of the First International Sakharov Conference on Physics, 1991 (Nova Science Publishers, New York, also available as astro-ph/9406045 (unpublished
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A. Mezhlumian and A. A. Starobinsky, Sakharov Memorial Lectures in Physics, in Proceedings of the First International Sakharov Conference on Physics, 1991 (Nova Science Publishers, New York, 1992), p. 1119; also available as astro-ph/9406045 (unpublished).
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(1992)
Sakharov Memorial Lectures in Physics
, pp. 1119
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Mezhlumian, A.1
Starobinsky, A.A.2
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