Large Scale Structure: Dynamics and Statistics

Abstract

The peculiar velocity of galaxies and galaxy clusters is the only dynamical probe of gravity on cosmic scales, which makes it a crucial tool in studying gravitational instability, mass distributions and density fluctuations on large scales. In this dissertation, I present the work we did in estimating the cosmic peculiar velocity field. We introduce a new method of estimating peculiar velocities from kinetic Sunyaev-Zel'dovich (kSZ) effect using deep learning neural networks to simplify the complicated calculation steps in the conventional method. We explore the feasibility of applying the formalism to future kSZ observations by testing it with multiple noise models using numerical simulations designed for these purposes. We further discuss an analysis of the two-point peculiar velocity correlation function using data from both observations and simulations. We find a non-Gaussian distribution of the cosmic variance of the correlation function, which makes the peculiar velocity correlation function less than ideal as a probe of large-scale structure. To solve this problem, we develop an improved method for calculating the parallel and perpendicular velocity correlation functions directly from peculiar velocity surveys using maximum-likelihood estimators. The central feature of this method is the use of a position-dependent weighting scheme in order to reduce the contribution of nearby galaxies, which are typically overrepresented relative to more distant galaxies that occupy the volume of most surveys. We demonstrate that the correlation function calculated in this way is less susceptible to bias due to our particular location in the Universe and provides a better approximation of a Gaussian distribution errors than other velocity correlation functions. In addition, the position weighted parallel velocity correlation function provides stabler and tighter cosmological parameter constraints than other methods.