In this paper, we study the phase space of cosmological models in the context of Einstein-Gauss-Bonnet theory. More specifically, we consider a generalized dynamical system that encapsulates the main features of the theory and for the cases that this is rendered autonomous, we analyze its equilibrium points and stable and unstable manifolds corresponding to several distinct cosmological evolutions. As we demonstrate, the phase space is quite rich and contains invariant structures, which dictate the conditions under which the theory may be valid and viable in describing the evolution Universe during different phases. It is proved that a stable equilibrium point and two invariant manifolds leading to the fixed point, have both physical meaning and restrict the physical aspects of such a rich in structure modified theory of gravity. More important we prove the existence of a heteroclinic orbit which drives the evolution of the system to a stable fixed point. However, while on the fixed point the Friedman constraint corresponding to a flat Universe is satisfied, the points belonging to the heteroclinic orbit do not satisfy the Friedman constraint. We discuss the origin of this intriguing issue in some detail.

中文翻译：

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爱因斯坦-高斯-博内宇宙学的自主动力系统

在本文中，我们在爱因斯坦-高斯-博内理论的背景下研究了宇宙学模型的相空间。更具体地说，我们考虑了一个概括了该理论主要特征的广义动力系统，对于使其具有自主性的情况，我们分析了它的平衡点以及对应于几种不同宇宙学演化的稳定和不稳定流形。正如我们所证明的，相空间非常丰富并且包含不变结构，这决定了该理论在描述不同阶段的演化宇宙时可能有效和可行的条件。证明了一个稳定的平衡点和两个通向不动点的不变流形，既具有物理意义又限制了这种结构丰富的修正引力理论的物理方面。更重要的是，我们证明了异宿轨道的存在，它驱动系统演化到一个稳定的不动点。然而，虽然在不动点上满足对应于平坦宇宙的弗里德曼约束，但属于异宿轨道的点不满足弗里德曼约束。我们详细讨论了这个有趣问题的起源。