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arXiv 0707.0585gr-qcastro-phhep-th
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宇宙演化早期的波函数

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

Sergei P. Maydanyuk

备注：
19 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
发表信息：
Eur.Phys.J.C57:769-784,2008
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摘要：

在Friedmann-Robertson-Walker度规框架下构建的量子宇宙学模型中，宇宙的成核及其进一步膨胀被描述为在非零（或零）能量下通过具有小和大尺度因子$a$值的区域之间的有效势垒的隧穿跃迁。描述这种隧穿的方法包括构造一个满足适当边界条件的波函数。边界条件的定义有多种方法，导致对势垒穿透率和隧穿时间的不同估计。为了尽可能精确地描述从隧穿区的逃逸，并明确地基于其两个部分解构造总波函数，我们使用隧穿边界条件，即总波函数必须仅表示从势垒逃逸点处的出射波，其中引入了以下波的定义：波由波函数表示，其模量在比例因子$a$的变化下变化最小。我们构造了一种新的方法来直接非半经典计算宇宙的总定态波函数，分析了该波函数在隧穿区、逃逸点附近和渐近区的行为，并估计了势垒穿透率.我们观察到波函数的模在外部区域从转折点开始的振荡，随着$a$的增加而减小，这在半经典计算中没有显示。这种振荡的周期随着$a$的增加而均匀地减小，可以作为宇宙膨胀的完全量子动力学特征。

英文摘要：

In 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.

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