413 research outputs found

    Quantum Perfect-Fluid Kaluza-Klein Cosmology

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    The perfect fluid cosmology in the 1+d+D dimensional Kaluza-Klein spacetimes for an arbitrary barotropic equation of state p=nρp= n \rho is quantized by using the Schutz's variational formalism. We make efforts in the mathematics to solve the problems in two cases. For the first case of the stiff fluid n=1n=1 we exactly solve the Wheeler-DeWitt equation when the dd space is flat. After the superposition of the solutions we analyze the Bohmian trajectories of the final-stage wave-packet functions and show that the flat dd spaces and the compact DD spaces will eventually evolve into finite scale functions. For the second case of n1n \approx 1, we use the approximated wavefunction in the Wheeler-DeWitt equation to find the analytic forms of the final-stage wave-packet functions. After analyzing the Bohmian trajectories we show that the flat dd spaces will be expanding forever while the scale function of the contracting DD spaces would not become zero within finite time. Our investigations indicate that the quantum effect in the quantum perfect-fluid cosmology could prevent the extra compact DD spaces in the Kaluza-Klein theory from collapsing into a singularity or that the "crack-of-doom" singularity of the extra compact dimensions is made to occur at t=t=\infty.Comment: Latex 18 pages, add section 2 to introduce the quantization of perfect flui

    Troubles with quantum anistropic cosmological models: Loss of unitarity

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    The anisotropic Bianchi I cosmological model coupled with perfect fluid is quantized in the minisuperspace. The perfect fluid is described by using the Schutz formalism which allows to attribute dynamical degrees of freedom to matter. A Schr\"odinger-type equation is obtained where the matter variables play the role of time. However, the signature of the kinetic term is hyperbolic. This Schr\"odinger-like equation is solved and a wave packet is constructed. The norm of the resulting wave function comes out to be time dependent, indicating the loss of unitarity in this model. The loss of unitarity is due to the fact that the effective Hamiltonian is hermitian but not self-adjoint. The expectation value and the bohmian trajectories are evaluated leading to different cosmological scenarios, what is a consequence of the absence of a unitary quantum structure. The consistency of this quantum model is discussed as well as the generality of the absence of unitarity in anisotropic quantum models.Comment: Latex file, 18 pages. To appear in General Relativity and Gravitatio

    Dynamical Vacuum in Quantum Cosmology

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    By regarding the vacuum as a perfect fluid with equation of state p=-rho, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom. 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. It turns out 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.Comment: Latex, 19 pages, to appear in Gen. Rel. Gra

    Quantum cosmological perfect fluid models

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    Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state p=αρp = \alpha\rho are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for αα>1\alpha \alpha > - 1.Comment: Latex file, 12 pages. New paragraphs in the Introduction and Conclusion, and other minor corrections in the text and in some formulas. Accepted for publication in General Relativity and Gravitatio

    A Quantum Cosmological Model With Static and Dynamic Wormholes

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    Quantization is performed of a Friedmann-Robertson-Walker universe filled with a conformally invariant scalar field and a perfect fluid with equation of state p=αρp=\alpha \rho. A well-known discrete set of static quantum wormholes is shown to exist for radiation (α=1/3\alpha =1/3), and a novel continuous set is found for cosmic strings (α=1/3\alpha = -1/3), the latter states having throat radii of any size. In both cases wave-packet solutions to the Wheeler-DeWitt equation are obtained with all the properties of evolving quantum wormholes. In the case of a radiation fluid, a detailed analysis of the quantum dynamics is made in the context of the Bohm-de Broglie interpretation. It is shown that a repulsive quantum force inversely proportional to the cube of the scale factor prevents singularities in the quantum domain. For the states considered, there are no particle horizons either.Comment: LaTex file, 13 pages. To appear in General Relativity and Gravitatio
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