标题： 永恒膨胀的反弹完成机制 显示英文标题

标题： Bouncing completion of eternal inflation

摘要： 利用纯粹的运动学论证，Borde-Guth-Vilenkin（BGV）定理指出，任何平均膨胀率为正的最大时空都是测地线不完备的，因此过去永恒膨胀必然存在奇异性。 最近，通过将其应用于新的模型和/或质疑时空最大性假设，关于该定理广义性的讨论重新浮出水面。 在本文中，我们使用非共动观察者的参考系及其运动学性质，以探究这种可能的奇异开端的本质。 以空间平坦的de Sitter（dS）时空作为实验室，这种方法使我们能够在一般空间平坦的Friedmann-Lemaître-Robertson-Walker（FLRW）几何情况下穷尽所有受BGV定理约束的可能性。 我们证明，要么存在标量或平行传播曲率奇异性，要么时空必须是过去的渐近dS（当尺度因子变为零时哈勃参数有确定的非零极限，从而排除某些循环模型），才能可扩展。 我们能够在此局部扩展中不违反零能条件，并且表明此扩展必须包含反弹。 这是一个基于纯粹运动学论证和直觉的数学结果。 还讨论了此类扩展的可能物理实现。 作为副产品，我们提出了一种覆盖整个de Sitter时空的新图表。 显示英文摘要

摘要： Using a purely kinematical argument, the Borde-Guth-Vilenkin (BGV) theorem states that any maximal space-time with average positive expansion is geodesically incomplete, hence past eternal inflation would be necessarily singular. Recently, discussions about the broadness of this theorem have been resurfaced by applying it to new models and/or challenging the space-time maximality hypothesis. In the present work, we use reference frames of non co-moving observers and their kinematical properties in order to inquire into the nature of such possible singular beginnings. Using the spatially flat de Sitter (dS) space-time as a laboratory, this approach allows us to exhaust all possibilities bounded by the BGV theorem in the case of general spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) geometries. We show that either there exists a scalar or parallelly propagated curvature singularity, or the space-time must be past asymptotically dS (with a definite non-zero limit of the Hubble parameter when the scale factor becomes null, hence excluding certain cyclic models) in order to be extensible. We are able to present this local extension without violating the null energy condition, and we show that this extension must contain a bounce. This is a mathematical result based on purely kinematical arguments and intuition. The possible physical realization of such extensions are also discussed. As a side product, we present a new chart that covers all de Sitter space-time.