标题： 低频引力背景辐射的自洽解 显示英文标题

标题： Self-consistent solutions for low-frequency gravitational background radiation

摘要： 我们在Brill-Hartle类型的近似下，研究了在Einstein-de Sitter背景中，线性引力波的叠加对背景的反作用，直到波幅的小参数的二阶项$h_{ik}$。 波幅被假设为形成一个均匀且各向同性的随机过程。 没有对波长做出任何限制。 有效应力-能量张量$T^{e}_{\mu\nu}$是根据该过程的相关函数计算得出的。 我们特别讨论了$T^{e}_{\mu\nu}$是背景度规的主要激发的情况。 除了Tolman辐射宇宙外，还存在一个尺度因子类似于de Sitter宇宙的解，其中$p = -\rho$作为有效状态方程。 显示英文摘要

摘要： We study in a Brill-Hartle type of approximation the back-reaction of a superposition of linear gravitational waves in an Einstein-de Sitter background up to the second order in the small wave amplitudes $h_{ik}$. The wave amplitudes are assumed to form a homogeneous and isotropic stochastic process. No restriction for the wavelengths is assumed. The effective stress-energy tensor $T^{e}_{\mu\nu}$ is calculated in terms of the correlation functions of the process. We discuss in particular a situation where $T^{e}_{\mu\nu}$ is the dominant excitation of the background metric. Apart from the Tolman radiation universe, a solution with the scale factor of the de Sitter universe exists with $p = -\rho$ as effective equation of state.