Non-Equilibrium Aspects of Relic Neutrinos: From Freeze-out to the   Present Day
  In this dissertation, we study the evolution and properties of the relic (or cosmic) neutrino distribution from neutrino freeze-out at $T=O(1)$ MeV through the free-streaming era up to today, focusing on the deviation of the neutrino spectrum from equilibrium. In particular, we demonstrate the presence of chemical non-equilibrium that continues to the present day. The work naturally separates into two parts. The first focuses on aspects of the relic neutrinos that can be explored using conservation laws. The second part studies the neutrino distribution using the full general relativistic Boltzmann equation.   Part one begins with an overview of the history of the Universe, from just prior to neutrino freeze-out up through the present day, placing the history of cosmic neutrino evolution in its proper context. Motivated by the Planck CMB measurements of the effective number of neutrinos, we derive those properties of neutrino freeze-out that depend only on conservation laws and are independent of the details of the scattering processes. Part one ends with a characterization of the present day neutrino spectrum as seen from Earth.   The second part of this dissertation focuses on the properties of cosmic neutrinos that depend on the details of the neutrino reactions, as is necessary for modeling the non-thermal distortions from equilibrium and computing freeze-out temperatures. We detail a new spectral method for solving the Boltzmann equation, based on a dynamical basis of orthogonal polynomials, as well as an improved procedure for analytically simplifying the corresponding scattering integrals for subsequent numerical computation. We apply these novel solution methods to solve the Boltzmann equation through the neutrino freeze-out period and perform parametric studies of the dependence of neutrino freeze-out on standard model parameters. 
Jeremiah Birrell
nucl-th astro-ph.CO hep-ph