BKL动力学和各向异性天空模式的随机化
Stochastization of BKL dynamics and Anisotropic Sky Patterns
摘要：
分析了$4=3+1$时空维中宇宙学台球的动力学;在台球映射的大量迭代之后，在随机极限内表征了不同的统计映射。根据映射中Weyl反射的内容，建立了新的不变测度密度，对于包含对称壁的台球系统也是如此，这解释了爱因斯坦场方程解中非振荡标度因子的符号变化.在[Phys. Rev. D83，044038（2011）]中提出的大台球和小台球之间的统计等价性，在这里通过小台球概率的这些新定义来证明。进一步的新类别的BKL概率也已被定义，特别是对于单变量映射和双变量映射，对于早期的BKL动态，对于随机化的BKL动态和对于完全随机化的动态，对于大台球和小台球。的轨迹已被分类，根据这些新的概率，和不同规格的概率比较类的初始条件已分配的随机化的动态。因此，有可能建立一个定义的BKL概率的unconcernented动态的大台球，不同的模式外尔反射编码。因此，对于每个纪元中给定数量的历元发生的BKL概率的统计描述，进一步由这些纪元中包含的外尔反射的最可能数量来表征，这是从UPHP上的台球图的含义中推断出来的。这些新的建设已被认为是由随机限制的BKL动态的各向异性的观测值之间的连接的确定。
英文摘要：
The dynamics of cosmological billiards in $4=3+1$ spacetime dimensions is analyzed; the different statistical maps are characterized within the stochastic limit, reached after a large number of iterations of the billiard maps. New densities of invariant measures have been established, also for billiard systems which contain symmetry walls, according to the content of Weyl reflections in the maps, which account for the change of sign of the non-oscillating scale factors in the solution to the Einstein field equations. The statistical equivalence between the big billiard and the small billiard, posed in [Phys. Rev. D83, 044038 (2011)], is here proven by means of these new definitions of probabilities for the small billiard. Further new classes of BKL probabilities have also been defined especially for the one-variable map and for the two-variable map, for the early-time BKL dynamics, for a stochastizing BKL dynamics and for a completely stochastized dynamics, both for the big billiard and for the small billiard. The trajectories have been classified according to these new probabilties, and different specifications of probabilties comparing classes of initial conditions have been assigned for the stochastization of the dynamics. As a result, is is possible to establish a definition of BKL probabilities for the unquotiented dynamics of the big billiard, where the different patterns of Weyl reflections are encoded. The statistical description of BKL probabilities for the occurrence of a given number of epochs in each era are therefore further characterized by the most probable number of Weyl reflections contained in such eras, which is inferred from the implications of the billiard maps on the UPHP. These new constructions have been considered for the determination of the connection between the observed values of anisotropy by a stochastic limit of the BKL dynamics.
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