Abstract
By regarding the vacuum as a perfect fluid with equation of state p = -ρ, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom, following modern ideas that the cosmological term is a manifestation of the vacuum energy. Instead of being postulated from the start, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can be naturally introduced. Taking the scale factor as the sole degree of freedom of the gravitational field, stationary and wave-packet solutions to the Wheeler-DeWitt equation are found, whose properties are studied. It is found that states of the Universe with a definite value of the cosmological constant do not exist. For the wave packets investigated, quantum effects are noticeable only for small values of the scale factor, a classical regime being attained at asymptotically large times.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
DeWitt, B. S. (1967). Phys. Rev.160, 1113.
Halliwell, J. A. (1991). In Quantum Cosmology and Baby Universes, S. Coleman, J. B. Hartle, T. Piran and S. Weinberg, eds. (World Scientific, Singapore).
Kolb, E. W., and Turner, M. S. (1994). The Early Universe(Addison-Wesley, New York).
Lima, J. A. S., and Maia, A., Jr. (1995). Phys. Rev. D52, 5628.
Vilenkin, A. (1994). Phys. Rev. D50, 2581, and references therein.
Schutz, B. F. (1970). Phys. Rev. D2, 2762; (1971). Phys. Rev. D4, 3559.
See, for example, S. W. Hawking (1986). In Quantum Gravity and Cosmology, H. Sato and T. Inami, eds. (World Scientific, Singapore); Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973). Gravitation(W. H. Freeman, San Francisco).
Lapchinskii, V. G., and Rubakov, V. A. (1977). Theor. Math. Phys.33, 1076.
Hajíček, P. (1986). Phys. Rev. D34, 1040; see also Beluardi, S. C., and Ferraro, R. (1995). Phys. Rev. D52, 1963.
Blyth, W. F., and Isham, C. J. (1975). Phys. Rev. D11, 768.
Tipler, F. J. (1986). Phys. Rep.137, 231.
Lemos, N. A. (1996). J. Math. Phys.37, 1449.
Feinberg, J., and Peleg, Y. (1995). Phys. Rev. D52, 1988.
Fil'chenkov, M. L. (1995). Phys. Lett. B354, 208.
Hildebrand, F. B. (1976). Advanced Calculus for Applications(Prentice Hall, Englewood Cliffs, NJ).
Rindler, W. (1977). Essential Relativity(Springer, New York).
Sciama, D. W. (1975). Modern Cosmology(Cambridge University Press, Cambridge)
Lemos, N. A. (1996). Phys. Lett. A221, 359.
Gradshteyn, I. S., and Ryzhik, I. M. (1980). Tables of Integrals, Series and Products(Corrected and Enlarged Edition, Academic, New York).
Christodoulakis, T., and Papadopoulos, C. G. (1988). Phys. Rev. D38, 1063.
Bateman Manuscript Project (1953). Higher Transcen dental Functions, vol. II, A. Erdélyi, ed. (McGraw-Hill, New York).
Rights and permissions
About this article
Cite this article
Alvarenga, F.G., Lemos, N.A. Dynamical Vacuum in Quantum Cosmology. General Relativity and Gravitation 30, 681–694 (1998). https://doi.org/10.1023/A:1018896900336
Issue Date:
DOI: https://doi.org/10.1023/A:1018896900336