Kinetic theory of cosmic baryon distribution functions in expanding space times

Let us start our considerations here from the cosmic era of baryonelectron (or proton-electron) recombination. In standard cosmology it is usually assumed that at the cosmic recombination era photons and matter, meaning electrons and protons, in this phase of the cosmic evolution, are dynamically and physically tightly bound to each other and undergo strong mutual interactions via Coulomb collisions and Compton collisions. With these conditions taken for granted, a pure thermodynamical equilibrium state appears to be guaranteed, implying that particles (protons and electrons) are Maxwell distributed in velocity-space and photons have a Planckian blackbody distribution in frequency. Looking a little more in detail on this relevant point, it is, however, by far not so evident that these assumptions really can be expected to be fulfilled during this period of cosmic evolution. This is because photons and particles are reacting very differently to the cosmological expansion; photons generally are considered to be cooling due to cosmologically being redshifted,1,2 while particles in first order are not directly feeling the expansion, unless they feel it adiabatically by mediation through numerous Coulomb collisions like they do in a box with subsonic expansion of its walls. The expanding walls with an expansion velocity V should keep in touch with the particles; meaning that slow particles with particle velocities < v V do not feel the expansion since not interacting with the moving walls, while those with velocities > v V feel it, since their reflection velocities when coming back from the wall is reduced, i.e. < v` v .