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I am just an interested layman in the field of cosmology. In the usual account of the development of the universe, it is stated that about 380.000 years after the big bang the electromagnetic radiation was in thermal equilibrium with matter.

Does this mean that the universe was (and maybe is) an isolated thermodynamic system that was (and is) in internal thermodynamic equilibrium? Further, it is stated that this radiation is seen in todays cosmic microwave background radiation corresponding to a perfect blackbody radiation with a temperature of 2.7K after the expansion of the universe. Could this expansion be considered as an adiabatic expansion of the radiation system?

Then the radiation supposedly decoupled from matter due to recombination of electrons with atomic nuclei. Does this mean that after this (and now) radiation and matter (on the average) are no longer in thermal (thermodynamic) equilibrium in the universe?

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Yes. You are completely right on all accounts. At one point you suggest the universe is still in thermodynamic equilibrium --- this is not the case. As you later point out, after recombination, photons are baryons do decouple. Once average densities become low enough that the diffusion time (the time it takes for things to transfer heat to each-other) is longer than the dynamical time (the time it takes things to move and interact gravitationally), sub-systems also separate (e.g. galaxies and galaxy clusters). Most things are now moving towards gravitational equilibrium (via collapse into filaments, clusters, galaxies, clouds, stars, planets, etc).

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    $\begingroup$ Can you perhaps explain what you mean by "diffusion time" and "dynamical time"? And what is "gravitational equilibrium"? $\endgroup$ – freecharly Nov 8 '16 at 5:50
  • $\begingroup$ @freecharly sorry about the jargon, I just added brief explanations but please let me know if that's still unclear. $\endgroup$ – DilithiumMatrix Nov 9 '16 at 18:08
  • $\begingroup$ "DilithiumMatrix- Thanks! Now I understand better. $\endgroup$ – freecharly Nov 9 '16 at 19:35

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