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An oscillating, compact Friedmann universe with a massive conformally coupled scalar field is studied in the framework of quantum cosmology. The scalar field is treated as a perturbation and we look for solutions of the Wheeler-DeWitt equation describing stable stationary states of the model. We assume that the previous sources of quantum instability that have been discussed in the literature (particle production, and tunnelling to zero size) are absent. We then show, under rather general assumptions, that a further source of quantum instability prevents the existence of stationary states with localized wave function in the direction of the scalar-field modes.
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We extend our analysis for scalar fields in a Robertson-Walker metric to the electromagnetic field and Dirac fields by the method of invariants. The issue of the relation between conformal properties and particle production is re-examined and it is verified that the electromagnetic and massless spinor actions are conformal invariant, while the massless conformally coupled scalar field is not. For the scalar field case it is pointed out that the violation of conformal simmetry due to surface terms, although ininfluential for the equation of motion, does lead to effects in the quantized theory.
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The origin of negative pressure fluid (the dark energy) is investigated in the quantum model of the homogeneous, isotropic and closed universe filled with a uniform scalar field and a perfect fluid which defines a reference frame. The equations of the model are reduced to the form which allows a direct comparison between them and the equations of the Einsteinian classical theory of gravity. It is shown that quantized scalar field has a form of a condensate which behaves as an antigravitating medium. The theory predicts an accelerating expansion of the universe even if the vacuum energy density vanishes. An antigravitating effect of a condensate has a purely quantum nature. It is shown that the universe with the parameters close to the Planck ones can go through the period of exponential expansion. The conditions under which in semi-classical approximation the universe looks effectively like spatially flat with negative deceleration parameter are determined. The reduction to the standard model of classical cosmology is discussed.
In this paper we analyze the Dark Matter problem and the distribution of matter through two different approaches, which are linked by the possibility that the solution of these astronomical puzzles should be sought in the quantum imprinting of the Universe. The first approach is based on a cosmological model formulated and developed in the last ten years by the first and third authors of this paper; the so-called Archaic Universe. The second approach was formulated by Rosen in 1933 by considering the Friedmann-Einstein equations as a simple one-dimensional dynamical system reducing the cosmological equations in terms of a Schroedinger equation. As an example, the quantum memory in cosmological dynamics could explain the apparently periodic structures of the Universe while Archaic Universe shows how the quantum phase concernts not only an ancient era of the Universe, but quantum facets permeating the entire Universe today.
We present a simplified dynamic-vacuum-energy model for a time-symmetric Milne-like universe. The big bang singularity in this simplified model, like the one in a previous model, is just a coordinate singularity with finite curvature and energy density. We then calculate the dynamic behavior of scalar metric perturbations and find that these perturbations destabilize the big bang singularity.
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