Determining the Thermodynamics of Cosmic Gases at World Times after the Matter Recombination

It is not evident and easy to understand how cosmic gases like H-atoms, after the recombination of cosmic electrons and protons to neutral atoms, do thermodynamically behave when being embedded in a universe with an ongoing Hubble-like expansion. The physical question namely, which then is not easy to answer, is, how cosmic gas atoms in fact do recognize this expansion of the cosmic 3Dspace. Contemporary mainstream cosmology takes for granted that gas atoms do react polytropically or even adiabatically to cosmic volume changes and thus they do get more and more tenuous and colder in accordance with gas- and thermo- dynamic laws. In this case, however, one has to face the relevant fact that cosmic gases at times of the recombination era are already nearly collisionless over scales of 10 AU. It is then questionable, how gases react to cosmic volume changes under such, nearly collision-free conditions. Therefore we derive in this chapture a kinetic transport equation to describe the evolution of the gas distribution function dependent on cosmic time and velocity space coordinates in this specific cosmological season. The competent, partial differential equation does not allow for a solution of the distribution function in form of a separation of the two variables and but instead one can independently find solutions for two velocity moments of i.e. the density and the pressure P of the gas. Then we show that using a special type of distribution functions, i.e. kappa distribution functions, for the cosmic gas we then can derive such functions as function of just 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. One obtains that the usual thermodynamics and gas dynamics does not hold anymore for this cosmic situation, and instead the gas develops into strongly nonthermal, non-Maxwellian distributions. This could become an interesting subject of further studies to see whether the non-Maxwellian electrons at the event of recombination give their recognizable imprints on spectral features of the CMB background radiation.