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


Other title
Type of item
Degree grantor
University of Alberta
Author or creator
Junaid, Muhammad
Supervisor and department
Prof. Dmitri Pogosyan (Department of Physics) University of Alberta
Examining committee member and department
Carlo Contaldi (Department of Physics) Imperial College London
Alexander Penin (Department of Physics) University of Alberta
Valeri Frolov (Department of Physics) University of Alberta
Richard Sydora (Department of Physics) University of Alberta
Department of Physics

Date accepted
Graduation date
Doctor of Philosophy
Degree level
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.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
M. Junaid and D. Pogosyan. Geometrical measures of non-gaussianity generated from single field inflationary models. PRD, 92(043505), 2015.

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