Examining Non-Gaussianities in 1+1 Dimensions

This thesis focuses broadly on how to measure Non-Gaussianity, the deviation of perturbations from statistical Gaussianity. Observationally constraining Primordial Non-Gaussianity (PNG) in galaxy surveys will help elucidate the physics of the early universe, but it is unknown precisely which combination of summary statistics at low redshift (power spectrum, bispectrum, etc.) carries the most information about PNG. Instead of the usual 3 dimensions, this thesis considers a scenario in a single dimension, with gravitationally interacting particles simulated via Lagrangian Perturbation Theory. However, the `perturbation theory' can be solved exactly in one dimension. In this one-dimensional toy model, it is possible to calculate the Fisher Matrix for cosmological parameters at field-level and compare the result to various summary statistics. This thesis first calculates the power spectrum and the bispectrum from an ensemble of 1000 1-dimensional simulations. Then the field-level Fisher Matrix is calculated for Omega_m and sigma_8, omitting different levels of matter streams to determine how much information is contained in the multi-stream regions. Finally, the field-level Fisher matrix is compared with that of the power spectrum at the smallest and largest scales. This exercise demonstrates how working in one dimension has the potential to bring more intuition to the three-dimensional case regarding where cosmological information is contained.