Non-linear evolution of density fluctuations in numerical cosmology

作为建立数值宇宙学基础的第一步，我们开发了一个用于经典场论的通用三维双曲方程求解器，并研究了原始密度涨落的非线性演化和真空态的相变导致的拓扑缺陷。对于后一个项目，我们借助数值宇宙学的无处不在的性质，解决了横跨宇宙学的各种问题，从来自磁区壁的引力波和轴子，到从碰撞的亚稳态弦建立超对称模型的动力学约束。此外，我们还开发了早期宇宙中光子的玻尔兹曼求解器，以施加密度涨落的初始条件。对于修正的引力理论，我们研究了理论中隐藏的标量引力的细节，以及观测约束对其理论参数的可能性。

As a first step of establishing the foundations of Numerical Cosmology, we developed a general-purpose three-dimensional hyperbolic equation solver for classical field theory, and studied the non-linear evolution of primordial density fluctuations and the topological defects appeared as a result of phase transition of the vacuum states. As for the latter project, we addressed a variety of issues lying across cosmology by virtue of the ubiquitous property of Numerical Cosmology, from the gravitational waves and axions from domain walls, to the dynamical constraints on the model building of supersymmetric models from the colliding meta-stable strings. In addition, we developed a Boltzmann solver for the photons in the early Universe to impose the initial conditions of the density fluctuations. As for the modified gravity theories, we investigated the details of the scalar gravity hidden in the theories, and the possibility of the observational constraints on their theoretical parameters.