标题： 线性化宇宙扰动的渐进行为 显示英文标题

标题： Asymptotics of linearized cosmological perturbations

摘要： 在宇宙学中，爱因斯坦-欧拉方程的均匀和各向同性解以及这些解的线性扰动扮演着重要的角色。 本文证明了标量扰动在背景模型初始奇点接近时以及在晚期时间的渐近行为的结果。 感兴趣的主方程是一个线性双曲方程，其系数仅依赖于时间。 在两种渐近区域中都得到了解的展开式。 在两种情况下都展示了如何通过渐近展开中的某些函数来对具有线性状态方程的一般解进行参数化。 对于一些非线性状态方程，发现晚期的渐近行为与线性情况下的行为在定性上有所不同。 显示英文摘要

摘要： In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the approach to the initial singularity of the background model and at late times. The main equation of interest is a linear hyperbolic equation whose coefficients depend only on time. Expansions for the solutions are obtained in both asymptotic regimes. In both cases it is shown how general solutions with a linear equation of state can be parametrized by certain functions which are coefficients in the asymptotic expansion. For some nonlinear equations of state it is found that the late-time asymptotic behaviour is qualitatively different from that in the linear case.