宇宙早期原初引力波的非线性相互作用

早期宇宙极端动态，但对其引力环境的描画在现阶段还相对粗犷。由于计算难度所限，解析分析基本以极度简化的 FRW 度规为准，仅在其上添加微扰。但是在我们宇宙的幼年期，由暴胀、相变或宇宙弦等诸多物理过程产生的大量原初引力波模由于空间度规的微小而聚集在一起，可以达到很高的能量密度，进而透过爱因斯坦方程的非线性相互影响，在不同的尺度间传递能量。换言之，对宇宙早期的准确理解避不开对引力波非线性作用的详细刻画，但是解析方法如上所述显得捉襟见肘。我们在本项目中提议改造近期针对致密天体引力波源开发的数值模拟代码，开拓数值相对论在宇宙学上的应用，回答如下三个具体问题：（1）原初引力波背景的非线性作用能否形成引力波湍流？（2）引力波的非线性相互作用对宇宙扰动功率谱有多大影响？（3）暴胀是否可以接受非均匀的初始条件？

While the early universe is undoubtedly extremely dynamic, our theoretical models for describing it is sorely lacking in sophistication. Due to computational difficulties, analytical studies had mostly relied on the vastly simplified FRW metric, adding perturbations at best. However, during the infancy of our universe, primordial gravitational wave modes excited by inflation, phase transition or cosmic strings are compactified by the small spatial extends (in terms of metric, not necessarily topologically compact) into such high densities, that they would unavoidably interact with each other via the Einstein equations' innate nonlinearity, passing energy between them as a result. Subsequently, an accurate description of the early universe cannot do away with a detailed understanding of the nonlinear interaction between gravitational waves, a task analytical studies seem to have fallen short of. Within the scope of this grant, we propose to evolve a simulation code developed for extracting gravitational wave signals from astrophysical compact binary sources, into one capable of cosmological studies, allowing numerical relativity to migrate into the realm of cosmology. We aim to answer the following three specific questions: (1) Can turbulence form out of gravitational wave nonlinear interactions? (2) How much of an impact do these nonlinear interactions have on the various cosmic perturbation power spectra? (3) Can inflation be launched out of highly inhomogeneous initial conditions?