标题： k=1 FLRW的圈量子宇宙学：反体积修正的影响 显示英文标题

标题： Loop quantum cosmology of k=1 FLRW: Effects of inverse volume corrections

摘要： 我们从两种可用的量子化方案的角度，考虑环量子宇宙学（LQC）中的k=1弗里德曼-勒梅特-罗伯逊-沃克（FLRW）模型。 我们关注量子化过程中所谓“逆修正”的存在。 我们推导了相应的量子约束算子，并详细研究了基于开放全息的两种不同量子化中量子哈密顿约束的自伴性问题。 此外，我们详细分析了所得的有效理论，特别关注诸如能量密度和膨胀等不同标量可观测量的有界性等问题。 我们表明，包含逆修正解决了先前形式的主要不良特性之一，即在完整（有效）相空间中反弹附近能量密度和膨胀的无界性。 我们简要评论了这一新特征可能带来的后果。 显示英文摘要

摘要： We consider the k=1 Friedman-Lemaitre-Robertson-Walker (FLRW) model within loop quantum cosmology (LQC), from the perspective of the two available quantization prescriptions. We focus our attention on the existence of the so called `inverse corrections' in the quantization process. We derive the corresponding quantum constraint operators, and study in detail the issue of the self-adjointness of the quantum Hamiltonian constraint for two different quantizations based on open holonomies. Furthermore, we analize in detail the resulting effective theories, paying special attention to issues such as the boundedness of different scalar observables such as energy density and expansion. We show that the inclusion of the inverse corrections solves one of the main undesirable features of the previous formalism, namely the unboundedness of the energy density and expansion near the bounce on the full (effective) phase space. We briefly comment on possible consequences of this new feature.