🚀 go-pugleaf

In article <92Nov4.112758edt.486@neuron.ai.toronto.edu> radford@cs.toronto.edu (Radford Neal) writes:

(Stuff deleted)
>I'm a bit surprised that the temperatures [of the photon and neutrino
backgrounds] are different.  I can believe
>that present photon/neutrino interactions are not sufficient to produce 
>equilibrium, but wouldn't it be sufficient for equilibrium to have been
>present in the early universe?  I'd think that both backgrounds would then
>cool at the same rate, as the universe expands.  Hmmm... maybe the two 
>backgrounds both cease to have significant interactions with anything 
>else at some point, but the points are different for the two...?
>
>    Radford Neal

You've got it just about right.  Here's the story as I understand it:
At very early times, the neutrinos and photons and everything else were
in equilibrium.  As the Universe cooled, the interactions that maintain
equilibrium between the neutrinos and the other stuff become very 
infrequent, and the neutrinos drop out of equilibrium.  They still cool
at the same rate as the rest of the matter, though, so they maintain the
same temperature for a while.  But then something happens.

When the temperature of the Universe drops below about 1 MeV, there are
no longer enough high-energy photons around to keep on producing electron-
positron pairs.  So the electrons and positrons can't stay in thermal
equilibrium with the photons.  It's no longer possible to produce them,
but they can still be destroyed by annihilating with each other.  That's
exactly what happens.  Almost all of the electrons and positrons are 
destroyed in the reaction e+ + e- -> photons.  This injects extra
energy into the photons and heats them up.  (Actually, the photon 
temperature doesn't increase; it just decreases more slowly than it
otherwise would.)  From that moment on the photons are hotter than
the neutrinos.

If you do all the calculations, you find that the ratio of neutrino
temperature to photon temperature is (4/11)^(1/3), which has got
to be one of the most unusual numerical factors in physics.

-Ted