The Cosmic Microwave Background Polarization

The aim of this thesis is to provide a phenomenological introduction to the polarization of the Cosmic Microwave Background and the physic behind it. Our work is organized in the following order: in Chapter 1 we will present some fundamental concept in modern Cosmology and in Chapter 2 we will introduce the statistical formalism that we will need for description of the CMB anisotropies. A description of the CMB, its relationship with the thermal history of the Universe and its most important properties will be given in Chapter 3, along with a dissertation about the temperature anisotropies and a qualitative explanation of the origin of these fluctuations. Chapter 4 will be devoted to Thomson scattering, how it can lead to a linear polarization pattern under certain conditions and the development of a mathematical formalism to describe a general polarization state. Finally, in Chapter 5 we will focus on the polarization of the CMB, we will build intuition about the possible causes of various polarization patterns generated by a single electron and the differences between them. Another formalism will be introduced in order to describe the polarization without the need of a specific reference frame and it will be used to explain the modulation of the polarization modes over the last scattering surface. We will then understand how the detection of a B-mode in the CMB can be interpreted as the footprint of a primordial gravitational wave and so a strong proof of the theory of inflation.