One-Point Matter PDF’s Beyond TopHat Filters

Abstract

In this thesis, I studied the one-point probability distribution function (PDF) for averaged matter densities over spherical cells, which can be used to non-perturbatively probe the large-scale structure of our universe. The PDF depends on a function, known as the filter/window function, which takes some weighted average over the observed matter density within each cell. This averaging allows one to study the density field as some smoothed function rather than discrete points. In order to consider filters of different kinds, the PDF’s are constructed numerically using Python code. The PDF is analytically modeled using a path integral framework. By considering a family of radial window functions interpolating between the TopHat and Gaussian filters in coordinate space, I investigated the sensitivity of the PDF to the shape of the window function. It was found that the sensitivity is rather mild suggesting that the PDF is robust against the precise choice of the filter. Effective field theory (EFT) corrections were included and used to examine how sensitive different filters are to short-scale physics. Similar to the PDF, the effects coming from short-scale physics appeared weakly dependent on the choice of filter, regardless of how smooth the filter’s boundary was. The contribution coming from aspherical fluctuations to the collapse dynamics of the cell were computed by comparing the numerical PDF to high-resolution N-body simulations. It was found that this contribution factorizes as a prefactor to the PDF, which is redshift independent, with the exception of smaller sized cells which display some mild redshift dependent shifting. These discrepancies are thought to be associated with two-loop corrections to the PDF. We expect this model to be flexible enough to study beyond the ΛCDM model and act as a probe for new fundamental physics.