标题： 弗里德曼-勒梅特宇宙及其演变 显示英文标题

标题： Friedmann-Lemaître universes and their metamorphoses

摘要： 我们分析了考虑流体参数和宇宙常数不同作用以及方程退化特性的弗里德曼-勒梅特宇宙的动力学。 我们发现弗里德曼-勒梅特系统可简化为四种定性不等价的规范形式，并写出所有可能产生稳定扰动的集合（“泛扰动”）。 这些集合的余维数最多为三。 然后我们描述了所有可能的依赖于参数的解及其在通过分歧集演化过程中转变为其他形式的情况，这些情况也得到了完整描述。 这一分析导致了一个由与余维数相关的新的参数决定的宇宙演化图景，在标准宇宙学中这些参数为零。 出现的泛扰解都是无奇点的，它们的其他特性也进行了讨论。 显示英文摘要

摘要： We analyze the dynamics of the Friedmann-Lema\^itre universes taking into account the different roles played by the fluid parameter and the cosmological constant, as well as the degenerate character of the equations. We find that the Friedmann-Lema\^itre system reduces to four qualitatively inequivalent normal forms and write down the sets of all stable perturbations that may result (the `versal unfoldings'). These sets are of small codimension up to three. We then describe all possible parameter-dependent solutions and their transfigurations to other forms during evolution through the bifurcation sets, these are also fully described. This analysis leads to a picture of cosmological evolution determined by new parameters related to codimension which are zero in standard cosmology. The emerging versal solutions are all free of singularities, while other properties of them are also discussed.