标题： 奇异点与空间弯曲的环量子宇宙学 显示英文标题

标题： Exotic singularities and spatially curved Loop Quantum Cosmology

摘要： 我们研究了过去和未来演化中$k = \pm 1$弗里德曼-罗伯逊-沃克模型以及圈量子宇宙学中出现的各种奇异类空奇点，使用了一个足够普遍的物态方程经验模型。 我们强调了这些奇点的内在曲率所扮演的非平凡角色，以及在普朗克尺度下浮现的新物理现象。 我们证明量子引力效应通常会解析所有强曲率奇点，包括大撕裂和大冻结奇点。 弱奇点（包括突然和大刹车奇点）在空间曲率为负时被量子引力忽略，正如之前对于平坦空间模型的研究结果一样。 有趣的是，对于封闭空间模型，在过去演化过程中存在一些情况，弱奇点可以被解析。 封闭空间模型表现出另一个新颖特征。 对于特定的一类物态方程，此模型在圈量子宇宙学中也显示出另一条物理分支，即一个与母分支分离的婴儿宇宙。 我们的分析将之前关于平坦模型中强曲率奇点解析的结果推广到了具有非零空间曲率的各向同性时空。 显示英文摘要

摘要： We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of $k = \pm 1$ Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for the equation of state. We highlight the non-trivial role played by the intrinsic curvature for these singularities and the new physics which emerges at the Planck scale. We show that quantum gravity effects generically resolve all strong curvature singularities including big rip and big freeze singularities. The weak singularities, which include sudden and big brake singularities are ignored by quantum gravity when spatial curvature is negative, as was previously found for the spatially flat model. Interestingly, for the spatially closed model there exist cases where weak singularities may be resolved when they occur in the past evolution. The spatially closed model exhibits another novel feature. For a particular class of equation of state, this model also exhibits an additional physical branch in loop quantum cosmology, a baby universe separated from the parent branch. Our analysis generalizes previous results obtained on the resolution of strong curvature singularities in flat models to isotropic spacetimes with non-zero spatial curvature.