论文标题
奇异定理对非词性宇宙大小的含义
Implications of the singularity theorem for the size of a nonsingular universe
论文作者
论文摘要
假设无效的收敛条件和全球双曲线，研究了没有初始奇异性的宇宙的一般特性。作为奇异定理的直接结果，具有过去被困表面的非词性宇宙的cauchy表面的普遍覆盖必须具有$ s^3 $的拓扑。此外，我们发现上面是通过无效测量学的仿射长度定义的非源性宇宙的仿射大小。在Friedmann-Lema-Robertson-Walker时空描述了非义时时期的一部分的情况下，我们发现该上限可以理解为相应的封闭DE Sitter Universe的仿射大小。假设我们的宇宙没有初始的奇异性，我们还根据最近观察到巴里昂声学振荡的观察结果确认了宇宙仿射大小的上限。
A general property of universes without initial singularity is investigated based on the singularity theorem, assuming the null convergence condition and the global hyperbolicity. As a direct consequence of the singularity theorem, the universal covering of a Cauchy surface of a nonsingular universe with a past trapped surface must have the topology of $S^3$. In addition, we find that the affine size of a nonsingular universe, defined through the affine length of null geodesics, is bounded above. In the case where a part of the nonsingular spacetime is described by Friedmann-Lemaître-Robertson-Walker spacetime, we find that this upper bound can be understood as the affine size of the corresponding closed de Sitter universe. We also evaluate the upper bound of the affine size of our Universe based on the trapped surface confirmed by recent observations of baryon acoustic oscillations, assuming that our Universe has no initial singularity.
