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

Persistent Link:
http://hdl.handle.net/10150/322969
Title:
Non-Equilibrium Aspects of Relic Neutrinos: From Freeze-out to the Present Day
Author:
Birrell, Jeremiah
Issue Date:
2014
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
Keywords:
Collision integral; Kinetic theory; Neutrino freezeout; Spectral method; Applied Mathematics; Boltzmann equation
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Rafelski, Johann

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleNon-Equilibrium Aspects of Relic Neutrinos: From Freeze-out to the Present Dayen_US
dc.creatorBirrell, Jeremiahen_US
dc.contributor.authorBirrell, Jeremiahen_US
dc.date.issued2014-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © 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.en_US
dc.description.abstractIn 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.en_US
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectCollision integralen_US
dc.subjectKinetic theoryen_US
dc.subjectNeutrino freezeouten_US
dc.subjectSpectral methoden_US
dc.subjectApplied Mathematicsen_US
dc.subjectBoltzmann equationen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorRafelski, Johannen_US
dc.contributor.committeememberRafelski, Johannen_US
dc.contributor.committeememberFleming, Sean P.en_US
dc.contributor.committeememberGlickenstein, David A.en_US
dc.contributor.committeememberPickrell, Douglas M.en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.