# Non-gaussian Statistics as a Probe of the Early Universe

Open Access
Author:
Nelson, Elliot Luke
Physics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 04, 2015
Committee Members:
• Sarah Elizabeth Shandera, Dissertation Advisor
• Martin Bojowald, Committee Member
• Eugenio Bianchi, Committee Member
• Donghui Jeong, Special Member
Keywords:
• cosmology
• inflation
• primordial perturbations
• cosmic microwave background
• statistics
• non-Gaussianity
• cosmic variance
Abstract:
We study effects from mode coupling or non-Gaussianity in the primordial curvature perturbations. For local-type non-Gaussianity, which couples fluctuations on very different scales, we study the influence of long-wavelength background modes on the statistical properties of short-scale modes in a finite volume such as the observable universe. We show that background modes can introduce a shift or bias to observed parameters, and quantify this influence for the primordial power spectrum $\Delta^2_\zeta$, non-Gaussianity parameter $f_{\rm NL}$, spectral index $n_s$, and dark matter halo power spectrum. We show that a non-Gaussian field with sufficiently strong coupling of modes on long and short scales will appear nearly Gaussian in typical subvolumes that are sufficiently small, indicating the naturalness of the weakly non-Gaussian local ansatz. In light of these results, we discuss the implications of observing the universe in a finite volume for our understanding of inflation. In addition to studying the statistical properties of curvature perturbations on a fixed spatial slice at the end of inflation, we also consider an example of mode coupling arising from nonlinear inflationary dynamics. A non-vacuum initial state at the onset of inflation can allow scalar curvature perturbations to couple strongly to long-wavelength tensor perturbations, resulting in an anisotropic contribution to the power spectrum of density perturbations.