论文标题
在晶格中的本质平坦宇宙学模型上
On the intrinsically flat cosmological models in a lattice
论文作者
论文摘要
在本手稿中，我们研究了本质上平坦的（空格）空间作为可行的宇宙学模型。我们表明它们具有自然的几何结构，适合描述整个空间中形成周期性模式的不均匀物质分布。我们证明定理的本地表示以及在这些周期性边界条件下的爱因斯坦方程的存在和独特性。我们还发现了一类有趣的精确解决方案，该解决方案说明了这种空间在宇宙学中的适用性，其早期行为接近均匀性和各向同性，以及较晚的时间方面，在物质分布中具有峰值和空隙。
In this manuscript we investigate the intrinsically flat (space-flat) spacetimes as viable cosmological models. We show that they have a natural geometric structure which is suitable to describe inhomogeneous matter distributions forming a periodic pattern throughout the space. We prove theorems for their local representation and for existence and uniqueness of the Einstein's equations with these periodic boundary conditions. We also find an interesting class of exact solutions, which illustrates the applicability of such spacetimes in cosmology, with an early time behavior close to homogeneity and isotropy and a late time aspect with peaks and voids in the matter distribution.
