arXiv 1301.45692013-01-19gr-qcastro-ph.COhep-thquant-ph

大爆炸的完全量子模型

A fully quantum model of Big Bang

Sergei P. Maydanyuk, Antonino Del Popolo, Vladislav S. Olkhovsky

备注：: 29 pages, 12 figures. arXiv admin note: substantial text overlap with arXiv:0812.5081, arXiv:1005.5447, arXiv:0707.0585

摘要：

本文研究了具有正宇宙学常数和辐射的封闭Friedmann-Robertson-Walker量子化模型。为了分析渐近deSitter、暴胀宇宙产生的隧穿几率随辐射能量的变化，本文提出了强场中传播的"自由"波的新定义。在此基础上，对隧道边界条件进行了修正，用全量子定态方法计算了势垒的穿透率和反射率。第一次考虑了入射波和反射波之间的非零干涉，这在宇宙学势中起着重要作用，可以用量子力学中的势垒非定域性来解释。在整个辐射能区中，暴胀宇宙诞生的隧穿几率与半经典方法得到的结果接近。第一次确定了来自屏障的反射（在接近屏障高度的辐射能量处，其基本上在1上不同）。所提出的方法可以很容易地推广到具有任意形状的障碍的宇宙学模型，这已被证明是FRW模型与包括Chaubergin气体。结果对势垒高度的变化是稳定的，对势垒高度以下的所有系数和能量的精度为11 - 18位。

英文摘要：

In the paper the closed Friedmann-Robertson-Walker model with quantization in the presence of the positive cosmological constant and radiation is studied. For analysis of tunneling probability for birth of an asymptotically deSitter, inflationary Universe as a function of the radiation energy a new definition of a "free" wave propagating inside strong fields is proposed. On such a basis, tunneling boundary condition is corrected, penetrability and reflection concerning to the barrier are calculated in fully quantum stationary approach. For the first time non-zero interference between the incident and reflected waves has been taken into account which turns out to play important role inside cosmological potentials and could be explained by non-locality of barriers in quantum mechanics. Inside whole region of energy of radiation the tunneling probability for the birth of the inflationary Universe is found to be close to its value obtained in semiclassical approach. The reflection from the barrier is determined for the first time (which is essentially differs on 1 at the energy of radiation close to the barrier height). The proposed method could be easily generalized on the cosmological models with the barriers of arbitrary shape, that has been demonstrated for the FRW-model with included Chaplygin gas. Result is stable for variations of the studied barriers, accuracy are found to be 11--18 digits for all coefficients and energies below the barrier height.

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