标题： 反弹多元宇宙的过去不完整性 显示英文标题

标题： Past incompleteness of a bouncing multiverse

摘要： 根据经典广义相对论，宇宙多世界中的反德西特（AdS）气泡最终会终止于大挤压奇点。然而，有人推测，基本理论可能会解决这些奇点，并用无奇点的反弹代替它们。这可能对多世界的开始有重要影响。已知宇宙时空中的测地线是过去不完整的，只要测地线上的平均膨胀率为正，但如果不考虑测地线多次穿过大挤压AdS气泡的情况，这一点尚不清楚。我们在一个简单的多世界模型中研究了这个问题，其中时空由弗里德曼-罗伯特森-沃尔克（FRW）区域组成。结论是，即使存在AdS反弹，时空仍然是过去不完整的。 显示英文摘要

摘要： According to classical GR, Anti-de Sitter (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by nonsingular bounces. This may have important implications for the beginning of the multiverse. Geodesics in cosmological spacetimes are known to be past-incomplete, as long as the average expansion rate along the geodesic is positive, but it is not clear that the latter condition is satisfied if the geodesic repeatedly passes through crunching AdS bubbles. We investigate this issue in a simple multiverse model, where the spacetime consists of a patchwork of FRW regions. The conclusion is that the spacetime is still past-incomplete, even in the presence of AdS bounces.