So in our GR lecture, we studied the $\Lambda$CMB model. And we neglected interactions between different contents of the universe and we found the following: The universe was first dominated by radiation, then matter, and later on cosmological constant.

Now the assumption of neglecting interactions seems reasonable now, but as we go back in time it is not and that's why we refer to statistical mechanics (as is mentioned in the text below, emphasis by me).

What I don't understand is that if the universe reached a thermal equilibrium in the radiation dominated epoch, why isn't it anymore?

With the knowledge we have so far, we can extrapolate back into the history of the universe until the temperature becomes high enough that interactions allow significant interchanges among the energy components of the universe.Probing back further would require assumptions about the particle interactions and the nature of physical laws themselves. Nevertheless, this apparent drawback, when taken to the extremity, turns into an advantage. As particles interact more strongly and rapidly, they are more likely to achieve thermal equilibrium. Thanks to that, we can use the powerful concept of thermal equilibrium, which allows us to describe a huge system, i.e. the universe, with only a few thermodynamical parameters such as temperature and chemical potentials. It is remarkable how much further we can go when armed with statistical mechanics.


1 Answer 1


The universe was (and still is) expanding. As it expanded, the number density of photons (and of matter) decreased, and consequently the interaction rate between them decreased. Eventually it decreased to the point that the two species thermally decoupled.

  • $\begingroup$ I see. And so those photons are we we know today as the Cosmic Microwave Background, right? So would it be correct to say that the universe never settled in an equilibrium state. Instead, it just passed through it for an instantaneous moment and kept on cooling down? $\endgroup$
    – devCharaf
    Apr 22, 2020 at 16:29
  • $\begingroup$ @Pinkman98 Maybe this is an explanation: researchgate.net/publication/… $\endgroup$
    – J. H
    Apr 22, 2020 at 17:16
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    $\begingroup$ @Pinkman98 in a uniformly expanding universe, a fluid can be in equilibrium and still cool down (since the cooling is on account of the expansion, not the equilibration of the out-of-equilibrium fluid). $\endgroup$
    – bapowell
    Apr 22, 2020 at 17:19
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    $\begingroup$ @Pinkman98 I'm not sure what you mean by "settled". If we skip past the GUT-scale physics we don't yet understand, the universe essentially started in a thermal equilibrium state, and adiabatically evolved through a series of successively cooler equilibrium states. "Equilibrium" doesn't mean that its properties stay the same as a function of time; any quasistatic process is a transition between equilibrium states that never leaves equilibrium in between. $\endgroup$ Apr 22, 2020 at 17:48
  • $\begingroup$ Thank you guys, It is much clear to me now :) $\endgroup$
    – devCharaf
    Apr 23, 2020 at 8:23

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