标题： 预测全局$CPT$对称宇宙中的空间曲率$Ω_K$ 显示英文标题

标题： Predicting spatial curvature $Ω_K$ in globally $CPT$-symmetric universes

摘要： 波义尔和图洛克的$CPT$对称宇宙模型认为，在大爆炸时宇宙是对称的，解决了宇宙学和粒子物理标准模型中的许多问题。 我们通过在宇宙末期引入对称条件来扩展这个模型，这些对称条件对允许的扰动模式施加了约束。 这些受约束的模式与闭合宇宙中全局空间几何所需的整数波矢量相冲突。 为了解决这一冲突，只有特定的曲率值是允许的，并且特别是曲率密度被限制为$\Omega_K \in \{-0.014, -0.009, -0.003, \ldots\}$，这与普朗克观测结果一致。 显示英文摘要

摘要： Boyle and Turok's $CPT$-symmetric universe model posits that the universe was symmetric at the Big Bang, addressing numerous problems in both cosmology and the Standard Model of particle physics. We extend this model by incorporating the symmetric conditions at the end of the Universe, which impose constraints on the allowed perturbation modes. These constrained modes conflict with the integer wave vectors required by the global spatial geometry in a closed universe. To resolve this conflict, only specific values of curvature are permissible, and in particular the curvature density is constrained to be $\Omega_K \in \{-0.014, -0.009, -0.003, \ldots\}$, consistent with Planck observations.