Fluctuations in the CMB through inflation

Abstract: The goal of this project is to gain a better understanding of the temperature fluctuations observed in the CMB. This goal is reached with the aid of a literature study. The report touches upon the origin of the CMB as well as how it is measured, mentioning and explaining relevant concepts such as recombination, photon decoupling, black body radiation, angular power spectrum etc. It is also specified that the temperature of the CMB is not uniform but varies slightly. The fact that these fluctuations show inhomogeneities at the early universe is emphasized as well as the need for a satisfying theory that explains said fluctuations. By presenting and employing inflation theory in combination with quantum mechanics, we show how such a theory can be obtained. Through extensive calculation we show how the primordial power spectrum for zero-point fluctuations during inflation is obtained and how it can be related to the time of recombination through a transfer function, thus explaining the existence of fluctuations in the CMB.