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Kinetic theory in the expanding universe. 1st paperback ed., Reprint of the 1988 original. (English) Zbl 1093.82002

Cambridge Monographs on Mathematical Physics. Cambridge: Cambridge University Press (ISBN 0-521-60746-9/pbk; 0-521-36050-1/hbk). viii, 149 p. (2004).
The aim of the present monograph is to provide a bridge between the formal mathematics for kinetic theory in general relativity and the practical cosmology interested in results obtained with a minimum of formalism. Thus, the book is concerned with the solution of the Boltzmann equation in the expanding universe for various cosmological processes. The equations are derived from first principles and solved as explicitly as possible.
The book starts with a brief survey of the basics of relativity, cosmodynamics and kinetic theory. Next, a simple one-component space system is studied in detail, which is characterized by the Boltzmann equation. The energy-momentum tensor is analysed, and an expression for the entropy production is found. This expression is equivalent to a formula used by Weinberger (1971) to show that conventional processes in the early universe generate only small amounts of entropy. Further, first the statistical mechanics of an initially thermal and chemical equilibrium system of stable particles and antiparticles is considered generally. The particles and antiparticles can be annihilated and created. But now, with decreasing system temperature, at a sufficient low temperature depending on the mass of lighter annihilation products, the initial particles and antiparticles cannot be reconstituted any more, and the system becomes unstable (generalized Lee-Weinberg problem).
Then, the presented theory is applied to specific problems. So the temporal variation of the distribution function of the initially heavier particles and antiparticles (of the problem mentioned above) is studied (original Lee-Weinberg problem (1977) for heavy neutral leptons (mass \(>\) 2 GeV) and light conventional neutrinos (mass \(<\) 50 eV)). Besides, the electron-positron annihilation into photons is investigated for a temperature region appropriate to helium production. Further, the role of unstable massive neutrinos for heating processes is discussed.
A next chapter deals with the consideration of the main physical phenomena of the cosmic recombination regime. Here especially the difference of the temperatures of the relativistic and non-relativistic components of the cosmic electron-proton-photon mixture after electron-positron annihilation are estimated.
The last chapter presents a simplified model of the primordial helium formation, which reproduces the main results of highly sophisticated computer calculations to within a few percent.
The treatment of the book is mainly self-contained, and the physical problems are presented with high pedagogical experience. This book is of interest to relativists, cosmologists, astrophysicists, particle physicists, and theoretical physicists in general.

MSC:

82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
83F05 Relativistic cosmology
85A40 Astrophysical cosmology
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
85-02 Research exposition (monographs, survey articles) pertaining to astronomy and astrophysics
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