标题： 暴胀宇宙学动力学中的混沌与普遍性 显示英文标题

标题： Chaos and Universality in the Dynamics of Inflationary Cosmologies

摘要： 我们描述了闭合暴胀宇宙学混沌动力学中的一种新的统计模式，该模式与哈密顿旋转运动能量和双曲运动能量部分的划分有关，在模型相空间中鞍点中心的线性邻域内。 访问鞍点中心邻域的轨道的双曲能量相对于初始条件的集合具有随机分布，但相关的直方图定义了一个形式为$p(x) = C x^{-\gamma}$的统计分布定律，几乎涵盖了所考虑的所有双曲能量范围。 我们提供了数值证据，表明$\gamma$确定了初始条件集合中分形盆地边界的维数。 该分布具有普遍性，因为它不依赖于模型的参数，并且具有尺度不变性。 我们讨论了这种普遍性对暴胀物理可能的物理后果。 分布形式为$p(x) = C x^{-\gamma}$，几乎涵盖了所考虑的所有双曲能量范围。 我们提供了数值证据，表明$\gamma$确定了初始条件集合中分形盆地边界的维数。 该分布具有普遍性，因为它不依赖于模型的参数，并且具有尺度不变性。 我们讨论了这种普遍性对暴胀物理可能的物理后果。 显示英文摘要

摘要： We describe a new statistical pattern in the chaotic dynamics of closed inflationary cosmologies, associated with the partition of the Hamiltonian rotational motion energy and hyperbolic motion energy pieces, in a linear neighborhood of the saddle-center present in the phase space of the models. The hyperbolic energy of orbits visiting a neighborhood of the saddle-center has a random distribution with respect to the ensemble of initial conditions, but the associated histograms define a statistical distribution law of the form $p(x) = C x^{-\gamma}$, for almost the whole range of hyperbolic energies considered. We present numerical evidence that $\gamma$ determines the dimension of the fractal basin boundaries in the ensemble of initial conditions. This distribution is universal in the sense that it does not depend on the parameters of the models and is scale invariant. We discuss possible physical consequences of this universality for the physics of inflation.tribution law of the form $p(x) = C x^{-\gamma}$, for almost the whole range of hyperbolic energies considered. We present numerical evidence that $\gamma$ determines the dimension of the fractal basin boundaries in the ensemble of initial conditions. This distribution is universal in the sense that it does not depend on the parameters of the models and is scale invariant. We discuss possible physical consequences of this universality for the physics of inflation.