In this work, the wave functions associated to the quantum relativistic universe, which is described by the Wheeler–DeWitt equation, are obtained. Taking into account different kinds of energy density, namely, matter, radiation, vacuum, dark energy and quintessence, we discuss some aspects of the quantum dynamics. In all these cases, the wave functions of the quantum relativistic universe are given in terms of the triconfluent Heun functions. We investigate the expansion of the universe using these solutions and found that the asymptotic behavior for the scale factor is [Formula: see text] for whatever the form of energy density is. On the other hand, we analyze the behavior at early stages of the universe and found that [Formula: see text]. We also calculate and analyze the transmission coefficient through the effective potential barrier.

中文翻译：

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量子相对论宇宙学：动力学解释和隧穿宇宙

在这项工作中，获得了与由 Wheeler-DeWitt 方程描述的量子相对论宇宙相关的波函数。考虑到不同种类的能量密度，即物质、辐射、真空、暗能量和精华，我们讨论了量子动力学的一些方面。在所有这些情况下，量子相对论宇宙的波函数都是根据三合流 Heun 函数给出的。我们使用这些解决方案研究宇宙的膨胀，发现无论能量密度的形式是什么，比例因子的渐近行为都是[公式：见文本]。另一方面，我们分析了宇宙早期的行为，发现[公式：见正文]。我们还计算和分析了通过有效势垒的传输系数。