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arXiv 2002.01974gr-qc
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具有辐射和广义Chaubergin气体的模型中早期宇宙的动力学

The dynamics of the early universe in a model with radiation and a generalized Chaplygin gas

G. A. Monerat, C. G. M. Santos, G. Oliveira-Neto, E. V. Corrêa Silva, L. G. Ferreira Filho

备注：
In that new version, we removed a section and four figures. It has, now, 30 pages and 13 figures
发表信息：
The European Physical Journal Plus volume 136, Article number: 34 (2021)
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摘要：

早期宇宙是通过一个空间超曲面具有正曲率的Friedmann-Robertson-Walker模型的量子化来模拟的。在这个模型中，宇宙充满了两种流体：辐射和广义的Chaubergin气体。这个模型的量化是按照J. A.惠勒和B。德威特利用Schutz的形式主义，时间概念被恢复，Wheeler-DeWitt方程转化为一个依赖于时间的薛定谔方程，它在一个有效势$V_{eff}$的作用下支配着早期宇宙的动力学。这种潜力取决于三个参数。根据这些参数的值，$V_{eff}$可能有两种不同的形状。$V_{eff}(a)$可具有势垒的形状或势垒后面的阱的形状。我们解决，数值上，适当的时间相关的薛定谔方程，并获得初始波函数的时间演化，这两种情况。这些波函数满足适当的边界条件。对于这两种形状的$V_{eff}$，我们计算隧穿概率，这是一个函数的平均动能与辐射能$E_m$和三个参数的广义Chaubergin气体：$α$，$A$和$B$。对于$V_{eff}$的两种形状，隧穿概率表明宇宙应该以$E_m$、$α$、$A$和$B$的最高可能值成核。最后，我们研究了波函数隧穿$V_{eff}$后的经典宇宙演化。计算表明，宇宙可能会从普朗克时代以暴胀阶段出现。

英文摘要：

The early universe is modeled through the quantization of a Friedmann-Robertson-Walker model with positive curvature of the spatial hypersurfaces. In this model, the universe is filled by two fluids: radiation and a generalized Chaplygin gas. The quantization of this model is made following the prescriptions due to J. A. Wheeler and B. DeWitt. Using the Schutz's 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 $V_{eff}$. That potential, depends on three parameters. Depending on the values of these parameters, $V_{eff}$ may have two different shapes. $V_{eff}(a)$ may have the shape of a barrier or the shape of a well followed by a barrier. We solve, numerically, the appropriate time dependent Schrödinger equation and obtain the time evolution of an initial wave function, for both cases. These wave functions satisfy suitable boundary conditions. For both shapes of $V_{eff}$, we compute the tunneling probability, which is a function of the mean kinetic energy associated to the radiation energy $E_m$ and of the three parameters of the generalized Chaplygin gas: $α$, $A$ and $B$. The tunneling probabilities, for both shapes of $V_{eff}$, indicates that the universe should nucleate with the highest possible values of $E_m$, $α$, $A$ and $B$. Finally, we study the classical universe evolution after the wavefunction has tunneled $V_{eff}$. The calculations show that the universe may emerge from the Planck era in an inflationary phase.

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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