Study of the Statistics of Cosmic Microwave Background Fluctuations

Abstract

Observations of Cosmic Microwave Background (CMB), radiation created shortly after the Big Bang and presents almost uniformly across the universe, are our most important information about relevant physics during the beginning of our universe. The slight variations in the temperature of CMB provide evidence for testing predictions from models of the very early phase. Arguably, one of the best candidate models of the very early universe is in ation, a period of exponential expansion. In this project, we review how the quantum uctuation in this era seeds the CMB pattern. We study the implications of the non-Gaussianity pro le of CMB temperature uctuation on the physical aspect of in ationary models. We calculate correlation functions that allow comparison with observations to constrain non-linear parameters of the non-Gaussianity under a power-series ansatz. Then, we discuss single- field consistency relation which shows how detecting a large three-point function could eliminate all single- field in ationary models of in ation. We also discuss multi- field consistency relations where a weak signal of a four-point function compared to the two-point function could rule out a large class of multi- field models. Finally, we mention the limitations of this approach.