论文标题
动力学系统中的动力学系统宇宙学
Dynamical systems in perturbative scalar field cosmology
论文作者
论文摘要
我们在3维\ emph {compact}状态空间上得出了一个新的\ emph {常规}动态系统，该系统描述了具有微小耦合标量场的相对论模型的空间平坦的Robertson-Walker几何形状的线性标量扰动。这使我们能够构建用数字说明的全球解决方案空间，在该空间中显示已知的解决方案可以驻留在特殊不变的集合上。我们还使用动力学系统方法来获得有关共同和均匀密度曲率扰动的新结果。最后，我们展示了如何将方法扩展到更通用的标量场电位。这导致了状态空间，其中具有指数电位的模型的状态空间似乎是不变边界集，从而说明了它们在日益复杂的宇宙学模型层次结构中作为构件的作用。
We derive a new \emph{regular} dynamical system on a 3-dimensional \emph{compact} state space describing linear scalar perturbations of spatially flat Robertson-Walker geometries for relativistic models with a minimally coupled scalar field with an exponential potential. This enables us to construct the global solution space, illustrated with figures, where known solutions are shown to reside on special invariant sets. We also use our dynamical systems approach to obtain new results about the comoving and uniform density curvature perturbations. Finally we show how to extend our approach to more general scalar field potentials. This leads to state spaces where the state space of the models with an exponential potential appears as invariant boundary sets, thereby illustrating their role as building blocks in a hierarchy of increasingly complex cosmological models.
