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

• Author / Creator

  Junaid, Muhammad

• 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.

• Subjects / Keywords

  • Inflation
  • Non-Gaussianity

• Graduation date

  Fall 2015

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R30G8Q

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.