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    Non-Equilibrium Aspects of Relic Neutrinos: From Freeze-out to the Present Day

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    Author
    Birrell, Jeremiah
    Issue Date
    2014
    Keywords
    Collision integral
    Kinetic theory
    Neutrino freezeout
    Spectral method
    Applied Mathematics
    Boltzmann equation
    Advisor
    Rafelski, Johann
    
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    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    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 and 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 first develop some geometry background concerning volume forms and integration on submanifolds that is helpful in computations. We then detail a new spectral method for solving the Boltzmann equation, based on a dynamical basis of orthogonal polynomials. Next, we detail an improved procedure for analytically simplifying the corresponding scattering integrals for subsequent numerical computation. Using this, along with the spectral method mentioned above, we solve the Boltzmann equation through the neutrino freeze-out period. Finally, we conclude by using our novel solution methods to perform parametric studies of the dependence of the neutrino freeze-out standard model parameters. This exploration is performed with the aim of recognizing mechanisms in the neutrino freeze-out process that are capable of leading to the measured value of the effective number of neutrinos.
    Type
    text
    Electronic Dissertation
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Applied Mathematics
    Degree Grantor
    University of Arizona
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