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arXiv 0704.2585gr-qc
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早期宇宙的动力学和具有辐射和Chaubergin气体的模型中暴胀的初始条件

The dynamics of the early universe and the initial conditions for inflation in a model with radiation and a Chaplygin gas

G. A. Monerat, G. Oliveira-Neto, E. V. Corrêa Silva, L. G. Ferreira Filho, P. Romildo, J. C. Fabris, R. Fracalossi, F. G. Alvarenga, S. V. B. Gonçalves

摘要:

早期宇宙的模型是通过正曲率的弗里德曼-罗伯逊-沃克模型的量子化来完成的。物质内容包括两种流体:辐射和Chaubergin气体。这些模型的量化是由以下惠勒和德威特的处方。利用Schutz形式,时间概念被恢复,Wheeler-DeWitt方程转化为依赖于时间的薛定谔方程,在有效势$V_{ef}$的作用下,薛定谔方程决定了早期宇宙的动力学。利用有限差分法和Crank-Nicholson格式,在OCTAVE程序中实现了相应的含时薛定谔方程的求解,得到了初始波包的时间演化。该波包满足适当的边界条件。隧道概率的计算表明,宇宙可能从普朗克时代进入暴胀阶段。计算还表明,隧穿几率是初始波包的平均能量和与Chaubergin气体有关的两个参数的函数。我们还显示了这些结果和WKB近似得到的结果之间的比较。

英文摘要:

The modeling of the early universe is done through the quantization of a Friedmann-Robertson-Walker model with positive curvature. The material content consists of two fluids: radiation and Chaplygin gas. The quantization of these models is made by following the Wheeler and DeWitt's prescriptions. Using the Schutz formalism, the time notion is recovered and the Wheeler-DeWitt equation transforms into a time dependent Schrödinger equation, which rules the dynamics of the early universe, under the action of an effective potential $V_{ef}$. Using a finite differences method and the Crank-Nicholson scheme, in a code implemented in the program OCTAVE, we solve the corresponding time dependent Schrödinger equation and obtain the time evolution of a initial wave packet. This wave packet satisfies appropriate boundary conditions. The calculation of the tunneling probabilities shows that the universe may emerge from the Planck era to an inflationary phase. It also shows that, the tunneling probability is a function of the mean energy of the initial wave packet and of two parameters related to the Chaplygin gas. We also show a comparison between these results and those obtained by the WKB approximation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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