We analyze observational signatures arising from an epoch in cosmology corresponding to the simple harmonic universe, which consists of positive curvature, a negative cosmological constant, and one or more exotic matter sources with $-1<w=p/\rho \le -1/3$, which may then evolve or tunnel into an inflating and hot Big Bang phase. Particular relics specific to this class of models include spatial curvature with ${\Omega }_k<0$, modifications to the dark energy sector due to the presence of residual exotic matter, and the possibility that the cosmological constant may ultimately be negative. We review the constraints on the relevant parameters from Planck and other cosmological data sets, focusing on the roles of exotic matter and curvature, and we find that while sources with $w\approx -1$ tend to tighten the constraints on ${\Omega }_k$, matter with $w=-1/3$ can decouple curvature from the expansion history. For the case where the dark energy sector includes a negative cosmological constant, we use the experimental data to find an associated lower bound on the lifetime of the expansion of the Universe.

我们分析了与简谐宇宙相对应的宇宙学时代的观测特征，它由正曲率、负宇宙学常数和一个或多个具有以下特征的奇异物质源组成 $-1<瓦=磷/\rho \le -1/3$，然后可能演变或隧道进入膨胀和热的大爆炸阶段。此类模型特有的特殊遗物包括空间曲率和${\Omega }_{克}<0$，由于存在剩余的外来物质，以及宇宙常数最终可能为负的可能性，对暗能量部门的修改。我们回顾了普朗克和其他宇宙学数据集相关参数的约束，重点关注奇异物质和曲率的作用，我们发现，虽然来源与$瓦\approx -1$ 倾向于收紧约束 ${\Omega }_{克}$，与 $瓦=-1/3$可以将曲率与扩展历史解耦。对于暗能量扇区包含负宇宙学常数的情况，我们使用实验数据来找到宇宙膨胀寿命的相关下限。