In the recent article (2019 Phys. Rev. D 100 043533) a compact phase space generalization of the flat de Sitter cosmology has been proposed. The main advantages of the compactification is that physical quantities are bounded, and the quantum theory is characterized by finite dimensional Hilbert space. Furthermore, by considering the phase space, quantum description is constructed with the use SU(2) representation theory. The purpose of this article is to apply effective methods to analyze quantum dynamics of the model at the semi-classical regime. The analysis is performed both without prior solving of the quantum constraint and by extracting physical Hamiltonian of the model. At the effective level, the results of the two procedures are shown to be equivalent. We find a nontrivial behavior of the fluctuations around the recollapse of the Universe, which is distinct from what is found after quantization with the standard flat phase space. The behavior is reflected at the level of the modified Friedmann equation with quantum back-reaction effects, which is derived. Finally, a relation between quantum fluctuations in the minisuperspace model under consideration and the Bousso bound has been found. It has been shown that the Bousso bound can be violated for certain choices of semiclassical states.

在最近的文章 (2019 Phys. Rev. D 100 043533) 中，提出了扁平德西特宇宙学的紧凑相空间概括。紧化的主要优点是物理量是有界的，量子理论的特点是有限维希尔伯特空间。此外，通过考虑相空间，量子描述是用SU(2)表示理论构建的。本文的目的是应用有效的方法来分析模型在半经典状态下的量子动力学。该分析是在没有事先求解量子约束的情况下进行的，并且通过提取模型的物理哈密顿量来执行。在有效水平上，这两种程序的结果显示是等效的。我们发现了围绕宇宙重新坍缩的波动的非平凡行为，这与使用标准平坦相空间量化后发现的不同。该行为反映在具有量子逆反应效应的修正弗里德曼方程的水平上，这是导出的。最后，已经发现了所考虑的微型超空间模型中的量子涨落与布索界之间的关系。已经表明，对于半经典状态的某些选择，可以违反布索界。