标题： 加速十二面体宇宙上的波 显示英文标题

标题： Waves on accelerating dodecahedral universes

摘要： 我们研究在具有非平凡拓扑的常正曲率紧致3流形——庞加莱十二面体空间上，当尺度因子呈指数增长时的波传播。 我们证明了当t趋于无穷时存在一个极限状态，并得到了其解析表达式。 由于Sachs-Wolfe公式，深空由这个渐近轮廓来描述。 我们将柯西问题转化为由四元数计算确定的基本域上的混合问题。 我们进行了一种精确的计算方案：我们使用了一个在二面体二十面体群作用下不变的二阶有限元空间的变分方法。 显示英文摘要

摘要： We investigate the wave propagation on a compact 3-manifold of constant positive curvature with a non trivial topology, the Poincar\'e dodecahedral space, when the scale factor is exponentially increasing. We prove the existence of a limit state as t tends to infinity and we get its analytic expression. The deep sky is described by this asymptotic profile thanks to the Sachs-Wolfe formula. We transform the Cauchy problem into a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We perform an accurate scheme of computation: we employ a variational method using a space of second order finite elements that is invariant under the action of the binary icosahedral group.