Non-linear evolution of density fluctuations in numerical cosmology

作为建立数值宇宙学基础的第一步，我们发展了一个通用的三维经典场论双曲方程求解器，并研究了真空态相变引起的原初密度涨落和拓扑缺陷的非线性演化.至于后一个项目，我们解决了各种各样的问题，躺在宇宙学的数值宇宙学的无处不在的属性，从引力波和轴子域壁，从碰撞亚稳态弦的超对称模型的模型建立的动力学约束。此外，我们开发了一个玻尔兹曼求解器的光子在早期宇宙中施加的初始条件的密度波动。对于修正的引力理论，我们研究了隐藏在理论中的标量引力的细节，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.