Abstract
We find a Friedmann model with appropriate matter/energy density such that the solution of the Wheeler-DeWitt equation exactly corresponds to the classical evolution. The well-known problems in quantum cosmology disappear in the resulting coasting evolution. The exact quantum-classical correspondence is demonstrated with the help of the de Broglie-Bohm and modified de Broglie-Bohm approaches to quantum mechanics. It is reassuring that such a solution leads to a robust model of the universe, which agrees well with cosmological expansion indicated by SNe Ia data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. S. DeWitt, Phys. Rev. 160, 1113 (1967).
L. de Broglie, J. Phys. Rad., 6e serie, t. 8, 225 (1927).
D. Bohm, Phys. Rev. 85, 166, 180 (1952).
P. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, England, 1993).
D. Bohm and B. J. Hiley, The Undivided Universe (Routledge, London and New York, 1993).
M. V. John, Found. Phys. Lett. 15, 329 (2002); quantph/ 0102087.
R. Carroll, Quantum Theory, Deformation, and Integrability (North Holland, 2000).
P. K. Chattaraj (ed.), Quantum Trajectories (CRC Press, Taylor & Francis Group, Boca Raton, London, and New York, 2011).
R. E. Wyatt, Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics (Springer, New York, 2005).
D. He, D. Gao, and Q. Cai, Phys. Rev. D 89, 083510 (2014).
H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Massachusetts, 1980).
L. de Broglie, PhD thesis (University of Paris, 1924).
G. Bacciagaluppi and A. Valentini, Quantum Theory at the Crossroads: Reconsidering the 1927 solvay Conference (Cambridge University Press, New York, 2009).
C. D. Yang, Ann. Phys. (N.Y.) 319, 339 (2005); Int. J. Quantum Chem. 106, 1620 (2006); Ann. Phys. (N.Y.) 319, 444 (2005); Chaos, Solitons and Fractals 30, 342 (2006); Phys. Lett. A 372, 6240 (2008).
C.-C. Chou and R.E. Wyatt, Phys. Rev. E 74, 066702 (2006); J. Chem. Phys. 125, 174103 (2007).
Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys.125, 231103 (2006); J. Chem. Phys. 127, 197102 (2007).
A. S. Sanz and S. Miret-Artes, Chem. Phys. Lett. 445, 350 (2007); J. Chem. Phys. 127, 197101 (2007).
M. V. John, Ann. Phys. 324, 220 (2009); Ann. Phys. 325, 2132 (2010).
M. V. John and K. Mathew, Found. Phys. 43, 859 (2013).
J. A. Peacock, Cosmological Physics (Cambridge University Press, UK, 1999).
E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, 1990)
J. J. Halliwell Introductory lectures on quantum cosmology, Proc. Jerusalem Winter School on Quantum Cosmology, ed. T. Piran et al., World Scientific, Singapore, 1991) and references therein.
S. Dey and A. Fring, Phys. Rev. A 88, 022116 (2013).
E. A. Milne, Z. Astrophysik 6, 1 (1933); Relativity, Gravitation and World Structure (Oxford University Press, 1935).
M. V. John and K. Babu Joseph, Phys. Rev. D 61, 087304 (2000).
M. V. John and J. V. Narlikar, Phys. Rev. D 65, 043506 (2002).
M. V. John, Astrophys. J 630, 667 (2005).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
John, M.V. Exact classical correspondence in quantum cosmology. Gravit. Cosmol. 21, 208–215 (2015). https://doi.org/10.1134/S0202289315030044
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0202289315030044