Cosmic Baryon Kinetics Expressed by Its Velocity Moments over Times after the Matter Recombination

Abstract

Hans J.Fahr

As we are going to show here it is not easily understandable how cosmic gases like H-atoms, after the recombination of cosmic matter, do thermodynamically behave under the ongoing Hubble-like expansion of the universe. The question namely is not easy to answer; how cosmic gas atoms do in fact recognize the expansion of cosmic 3- space. Contemporary mainstream cosmology takes for granted that gas atoms do react polytropically or even adiabatically to cosmic volume changes and thus do get more and more tenuous and colder in accordance with gas- and thermo- dynamics. However, one has to face the fact that cosmic gases at the recombination era are already nearly collisionless over scales of 10 AU, and how gases react to cosmic volume changes under such conditions is not a trivial problem. We derive in this article a kinetic transport equation which describes the evolution of the gas distribution function f(t, v) in cosmic time t and velocity space of v. This partial differential equation does not allow for a solution in form a separation of the two variables t and v, but instead we can find solutions for two moments of f(v, t), i.e. the density n(t) and the pressure P(t). Then we show that using kappa-like functions for the cosmic gas we can derive such functions as function of their velocity moments, i.e. as functions of cosmic time. It means we understand the kinetic evolution of the cosmic gas by understanding the evolution in cosmic time of their moments.

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