Constraining Cosmological Models Using Non-Gaussian Perturbations in the Cosmic Microwave Background

We study non-Gaussian distributions in temperature fluctuations of the cosmic microwave background radiation. We introduce a novel way of measuring spatial variations in the fine-structure constant with these tools. We also lay out the method of measuring the first non-Gaussian moment using the three-point correlation function and an optimized estimator and apply these methods to the Planck CMB maps.