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.
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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
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DOI: https://doi.org/10.1023/A:1018896900336