The present work investigates some exact solutions of the gravitational wave equation in some widely used cosmological spacetimes. The examples are taken from spatially flat and closed isotropic models as well as Kasner metric which is anisotropic. Various matter distributions are considered, from the standard dust or radiation distribution to exotic matters like that with an equation of state \(P = - \frac{1}{3} \rho \). In almost all cases the frequency and amplitude of the wave are found to be decaying with evolution, except for a closed radiation universe where there is a resurgence of the waveform, consistent with the recollapse of the universe into the big crunch singularity.

目前的工作研究了一些广泛使用的宇宙学时空引力波动方程的一些精确解。这些示例取自空间平坦和封闭的各向同性模型以及各向异性的 Kasner 度量。考虑了各种物质分布，从标准尘埃或辐射分布到奇异物质，如状态方程\(P = - \frac{1}{3} \rho \)。在几乎所有情况下，都发现波的频率和振幅随着演化而衰减，除了一个封闭的辐射宇宙，那里的波形重新出现，与宇宙重新坍缩成大挤压奇点相一致。