Innovative Techniques to Address the Non-linearity of the Large Scale Structure of the Universe

To fully understand the non-linear evolution of the large scale structure of the Universe and to extract useful information from the large scale structure are key subjects of modern cosmology. In this dissertation, I am going to address the non-linearity of the Universe from two new perspectives.
One way to study the non-linearity is to study laments, which evolve non-linearly from the initial density fluctuations produced in the primordial Universe. In the first part of the dissertation, I am going to report the first detection of CMB (Cosmic Microwave Background) lensing by laments. We propose a phenomenological model to interpret the detected signal, and we measure how laments trace the matter distribution on large scales through lament bias. In the second part of the dissertation, I will present the deep learning method as a practical and accurate alternative to learning the gravitational structure formation of the Universe. We build two deep neural networks, the D3M model and the multi-scale deep sets model, to predict the non-linear structure formation of the Universe. Our extensive results have shown our models outperform the second-order
perturbation theory. I will also discuss our efforts in understanding the robustness of the trained deep learning model.