Cosmic Baryon Kinetics At Times After The Matter Recombination Analysed Via Its Velocity Moments

Abstract

Hans J. Fahr

The interesting aspect that we are paying attention to in this article here is the variation of the kinetic distribution function of particles subject to the early Hubble expansion of the universe. Some generally made assumptions namely are not fulfilled here: Neither does their distribution function stay a Maxwellian as expected for the cosmic begin, nor does the density of these particles simply fall off as expected in a homogeneous universe with the cosmic scale R = R(t) like n(t) = n0 (R0 /R)3 . Instead we do show here, that it is quite complicated to understand, how cosmic gases like the first H-atoms, after recombination out of the plasma state of cosmic matter, do thermodynamically behave under the ongoing omni-directional Hubble-like expansion dynamics of the universe. This is because there is no trivial answer to the question, how cosmic gas atoms do in fact recognize the expansion of cosmic 3- space they are embedded in. Standard mainstream cosmology takes for granted that gas atoms do react polytropically or even adiabatically to cosmic volume changes, consequently assuming that they do get more and more tenuous and colder in accordance with gas- and thermo- dynamic expectations. However, one has to face the fact that cosmic gases at the recombination era are already nearly collisionless over scales of 10 AU. How then do they recognize cosmic volume changes under such conditions and how do they react to it kinetically? 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 resulting partial differential equation does not allow for a solution in form a separation of the two variables t and v, but instead one obtains that f(v, t) is non-Maxwellian with its two lowest moments, i.e density n(t) and the pressure P(t), as pure functions of cosmic time t. Then we show that using kappa-like distribution functions f(t, v) = f κ (t, v) for the cosmic gas we can derive such functions as function of their velocity moments, i.e. as pure 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 nκ (t) and Pκ (t) with K = K(t).

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