Wave function of the Universe in the early stage of its evolution

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dc.creatorMaydanyuk, Sergei P.
dc.date2007-07-04
dc.date2008-11-28
dc.date.accessioned2026-07-07T12:13:35Z
dc.date.available2026-07-07T12:13:35Z
dc.descriptionIn quantum cosmological models, constructed in the framework of Friedmann-Robertson-Walker metrics, a nucleation of the Universe with its further expansion is described as a tunneling transition through an effective barrier between regions with small and large values of the scale factor $a$ at non-zero (or zero) energy. The approach for describing this tunneling consists of constructing a wave function satisfying an appropriate boundary condition. There are various ways for defining the boundary condition that lead to different estimates of the barrier penetrability and the tunneling time. In order to describe the escape from the tunneling region as accurately as possible and to construct the total wave function on the basis of its two partial solutions unambiguously, we use the tunneling boundary condition that the total wave function must represent only the outgoing wave at the point of escape from the barrier, where the following definition for the wave is introduced: the wave is represented by the wave function whose modulus changes minimally under a variation of the scale factor $a$. We construct a new method for a direct non-semiclassical calculation of the total stationary wave function of the Universe, analyze the behavior of this wave function in the tunneling region, near the escape point and in the asymptotic region, and estimate the barrier penetrability. We observe oscillations of modulus of wave function in the external region starting from the turning point which decrease with increasing of $a$ and which are not shown in semiclassical calculations. The period of such an oscillation decreases uniformly with increasing $a$ and can be used as a fully quantum dynamical characteristic of the expansion of the Universe.
dc.description19 pages, 21 files for 10 EPS figures, LaTeX svjour style. The Sec.2 (formalism of Wheeler-De Witt equation) is reduced. In Sec.3.1 definition of the outgoing wave from barrier is defined more accurately. In Sec.4.1 semiclassical calculations of wavew function and penetrability are performed and comparison with results in fully quantum approach is added
dc.identifierhttps://arxiv.org/abs/0707.0585
dc.identifierhttp://arxiv.org/abs/0707.0585
dc.identifierEur.Phys.J.C57:769-784,2008
dc.identifierdoi:10.1140/epjc/s10052-008-0723-2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210900
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectAstrophysics
dc.subjectHigh Energy Physics - Theory
dc.titleWave function of the Universe in the early stage of its evolution
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