一个简单的谐波宇宙
A Simple Harmonic Universe
摘要：
我们探索简单但新颖的弹跳解决方案的广义相对论，避免奇点。这些解需要曲率k=+1，并且有负的宇宙学项和-1 < w < -1/3的物质支持。在中等反弹的情况下（其中最大比例因子$a_+$与最小比例因子$a_-$的比率为${\cal O}(1)$），所示的解决方案是经典稳定的，并通过一个无限的反弹集循环。对于更极端的情况下，大$a_+/a_-$，解决方案仍然可以振荡许多次之前，经典的不稳定性，使他们的有效性制度的近似。在这种情况下，量子粒子的产生也最终导致偏离半经典广义相对论的有效范围，可能产生奇异的紧缩。我们简要地讨论了这些模型在现实宇宙学中的可能应用。
英文摘要：
We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k=+1, and are supported by a negative cosmological term and matter with -1 < w < -1/3. In the case of moderate bounces (where the ratio of the maximal scale factor $a_+$ to the minimal scale factor $a_-$ is ${\cal O}(1)$), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large $a_+/a_-$, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.
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