arXiv 1005.54472010-05-29gr-qcastro-ph.COhep-th

早期宇宙时空的共振结构

Resonant structure of space-time of early universe

Sergei P. Maydanyuk

备注：: 18 pages, 14 figures, 4 tables
发表信息：: Eur.Phys.J.Plus 126:76,2011
DOI：: 10.1140/epjp/i2011-11076-x

摘要：

本文提出了一种新的用于量子宇宙学问题的全量子方法，它描述了包从内阱向外穿透并隧穿任意形状势垒的过程。该方法允许确定波函数的幅度、相对于势垒的穿透性$T_{\rm bar}$和反射$R_{\rm bar}$（该方法的准确度：$|T_{\rm bar}+R_{\rm bar}-1| < 1 \cdot 10^{-15}$）、穿透系数（即，包从内部井向外穿透并具有其隧穿的概率）、振荡系数（描述包在内部井内部的振荡行为）。利用该方法，研究了在正宇宙学常数、辐射和广义Chaubergin气体组分存在的情况下，封闭的量子化Friedmann-Robertson-Walker模型中宇宙的演化.它是建立（第一次）：（1）振荡的渗透性的依赖于本地化的开始的包;（2）存在的共振值的能量辐射$E_{\rm rad}$，在该系数的渗透强烈增加。通过对这些结果的分析得出：（1）在定态和非定态量子模型中引入初始条件的必要性：（2）标度因子$a$存在一定的值，在这里宇宙膨胀的开始是最可能的;（3）宇宙膨胀的初始阶段，其半径不是连续变化的，但随后经过确定的离散值并在稍后的时间趋向于连续谱。

英文摘要：

A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes of wave function, penetrability $T_{\rm bar}$ and reflection $R_{\rm bar}$ relatively the barrier (accuracy of the method: $|T_{\rm bar}+R_{\rm bar}-1| < 1 \cdot 10^{-15}$), coefficient of penetration (i.e. probability of the packet to penetrate from the internal well outside with its tunneling), coefficient of oscillations (describing oscillating behavior of the packet inside the internal well). Using the method, evolution of universe in the closed Friedmann--Robertson--Walker model with quantization in presence of positive cosmological constant, radiation and component of generalize Chaplygin gas is studied. It is established (for the first time): (1) oscillating dependence of the penetrability on localization of start of the packet; (2) presence of resonant values of energy of radiation $E_{\rm rad}$, at which the coefficient of penetration increases strongly. From analysis of these results it follows: (1) necessity to introduce initial condition into both non-stationary, and stationary quantum models; (2) presence of some definite values for the scale factor $a$, where start of expansion of universe is the most probable; (3) during expansion of universe in the initial stage its radius is changed not continuously, but passes consequently through definite discrete values and tends to continuous spectrum in latter time.

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英文摘要：

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