Inhomogeneous anisotropic cosmology
Inhomogeneous anisotropic cosmology
复制标题
非均匀各向异性宇宙学
DOI：
10.1088/1475-7516/2016/10/022
复制
发表时间：
2016
影响因子：
6.4
通讯作者：
L. Senatore
中科院分区：
文献类型：
--
作者：
M. Kleban;L. Senatore
在均匀各向同性的Friedmann-Robertson-Walker宇宙学中，宇宙的拓扑结构决定了它的最终命运。如果满足弱能量条件，开放和平坦的宇宙一定会永远膨胀，而封闭的宇宙可能会重新塌陷成大裂缝。类似的说法也适用于均匀但各向异性的(比安奇)宇宙。在这里，我们证明了空间拓扑为“扁平”(包括环形)和“开放”(包括紧致双曲)的任意非均匀和各向异性宇宙，无论存在任意大的密度涨落和/或黑洞的形成，都必须至少在某个区域以一个正数的速率永远膨胀。因为3-流形的拓扑集是可数的，所以一个单一的整数决定了宇宙的最终命运，在特定意义上，大多数3-流形是“扁平的”或“开放的”。我们的结果对暴涨有重要的启示：如果有一个正的宇宙常数(或合适的暴胀势)和暴胀的初始条件，具有“平”或“开”拓扑的宇宙会在某些区域永远膨胀，其速度至少与de Sitter空间一样快，因此最终很有可能开始暴涨膨胀，无论暴涨能量的大小、初始不均匀和引力波的频谱和幅度如何。我们的结果对数值广义相对论也有重要意义，数值广义相对论通常使用周期(环形)边界条件。
In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with ``flat'' (including toroidal) and ``open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are ``flat'' or ``open''. Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with ``flat'' or ``open'' topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.