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This graduate/research level text is a self-contained exposition of the applications of kinetic theory to basic problems in modern cosmology, such as the role of stable and unstable massive neutrinos and the theory of cosmological helium production. There has been rapid development of the theory of the origin and evolution of the universe in recent years, stimulated in large part by new observations and theories in astrophysics and particle physics. This book takes a different approach and studies what can be concluded from the application to cosmological problems of kinetic theory and, in particular, the Boltzmann equation and its solutions. The book begins with a brief survey of the necessary relativity, cosmodynamics, and kinetic theory, before going on to discuss specific problems, such as the role of stable and unstable massive neutrinos, electron-poritron annihilation, and the theory of cosmological helium production. The focus is in obtaining both theoretical understanding and concrete numerical results.

The authors present a simplified model of helium synthesis in the early universe. The purpose of the model is to explain clearly the physical ideas relevant to the cosmological helium synthesis in a manner that does not overlay these ideas with complex computer calculations. The model closely follows the standard calculation, except that it neglects the small effect of Fermi-Dirac statistics for the leptons. The temperature difference between photons and neutrinos during the period in which neutrons and protons interconvert is also neglected. These approximations permit the expression of neutron-proton conversion rates in a closed form, which agrees to 10% accuracy or better with the exact rates. Using these analytic expressions for the rates, the authors reduce the calculation of the neutron-proton ratio as a function of temperature to a simple numerical integral. They also estimate the effect of neutron decay on the helium abundance. Their result for this quantity agrees well with precise computer calculations. Their semianalytic formulas are used to determine how the predicted helium abundance varies with such parameters as the neutron lifetime, the baryon-to-photon ratio, the number of neutrino species, and, a possible electronneutrino chemical potential. CONTENTS One feature of these early calculations was that they involved Dirac neutrinos. This doubled the number of neutrino states. This does not, however, aA'ect the final answer, since the factor of 2 is compensated in the relation between the e6'ective weak coupling constants and the neutron mean life.

We calculate exactly the one-loop finite-temperature effective potential for a self-interacting theory with a fixed U(1) charge. We analyze in detail two limits of this exact expression: the very-low-and very-high-temperature regimes. In the former we reproduce many standard results of the nonrelativistic Bose gas. In the high-temperature limit, we describe the effects, which can be striking, of nonzero charge on vacuum structure and critical temperatures. Generally we find that in order to accommodate the fixed charge a system tends to remain longer in a spontaneously broken phase.