Non-linear evolution of density fluctuations in numerical cosmology

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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.