Geometrical Measures of Non-Gaussianity Generated by Single Field Models of Inflation

Abstract

In this thesis we have compiled the study of geometrical non-Gaussianity generated by inflation along with necessary basics and background knowledge of inflationary universe. We effectively calculated the power spectrum and the bispectrum, as a measure of non-Gaussianity, using the approach laid by Maldacena. We developed a robust numerical technique to compute the bispectrum for different single field inflationary models that may even have some features in the inflationary potential. From the bispectrum, we evaluated the third order moments of scalar curvature perturbations in configuration space. We evaluate these moments analytically in the slow roll regime while we devised a numerical mechanism to calculated these moments even for non slow roll single field inflationary models with standard kinetic term that are minimally coupled to gravity. With help of these third order moments one can directly predict many non-Gaussian and geometrical measures of three dimensional distributions as well as two dimensional CMB maps in the configuration space. Thus, we have devised a framework to calculate geometrical measures, for example Minkowski functionals or skeleton statistic, generated by different single field models of inflation. Finally, we also calculated these configuration space moments for the two dimensional projection maps on the sky. We subtracted the monopole contribution of the two dimensional perturbation field from these moments so that we can estimate observable geometrical non-Gaussianity in CMB temperature maps generated by single field inflationary models.