Early universe: equilibrium before nucleosynthesis

[Davide82]

Hi.

I am studying the evolution of the universe.
In particular, I am reading the history of the universe happening just under a temperature of 100 MeV.
At this time, it is said that neutrons and protons are present along with some other particles: electrons, positrons, photons, neutrinos and anti-neutrinos.
They say the reactions which maintain kinetic equilibrium are:
$$e^- + e^+ \longleftrightarrow \gamma +\gamma$$
$$e^\pm + \gamma \longleftrightarrow e^\pm + \gamma$$
while the reactions which are responsible for both kinetic and chemical equilibrium are:
$$e^- + e^+ \longleftrightarrow \nu + \bar\nu$$
$$\nu + e^- \longleftrightarrow e^- + \nu$$
$$n + \nu_e \longleftrightarrow p + e^-$$
$$n + e^+ \longleftrightarrow p + \bar\nu_e$$
$$n \longleftrightarrow p + e^- + \bar\nu_e$$
I am wondering why reactions such as:
$$\nu + \bar\nu \longleftrightarrow \gamma + \gamma$$
$$p + e^+ \longleftrightarrow p + e^+$$
$$p + e^- \longleftrightarrow n + \nu_e + e^+ + e^-$$
are not taken into account.

 

[Davide82]

I am sorry that the TeX-interpreter doesn't seem to render my post...

 

[Davide82]

here it is in a more readable manner:

I am studying the evolution of the universe.
In particular, I am reading the history of the universe happening just under a temperature of 100 MeV.
At this time, it is said that neutrons and protons are present along with some other particles: electrons, positrons, photons, neutrinos and anti-neutrinos.
They say the reactions which maintain kinetic equilibrium are:

e- + e+ <---> photon + photon
e+- + photon <---> e+- + photon

while the reactions which are responsible for both kinetic and chemical equilibrium are:

e- + e+ <---> neutrino + anti-neutrino
neutrino + e- <---> e- + neutrino
n + neutrino(e) <---> p + e-
n + e+ <---> p + anti-neutrino(e)
n <---> p + e- + anti-neutrino(e)

I am wondering why reactions such as:

neutrino + anti-neutrino <---> photon + photon
p + e+ <---> p + e+
p + e- <---> n + anti-neutrino(e) + e+ + e-

are not taken into account.

 

[Davide82]

oh, now the first post with TeX has been fixed!

 

[JesseC]

I would assume the cross sections for those last three reactions to be negligibly small. Especially the ones involving neutrinos.

 

[Davide82]

I am still digging...
I believe the $$\nu + \bar\nu \longleftrightarrow \gamma + \gamma$$ is forbidden by the model.
The second maybe is not interesting because the other reactions already take care of the kinetic equilibrium of protons and electrons.
Since these reactions are brought up to make some calculations about their frequencies, maybe the last reaction is not needed because its cross section is similar to the other expressions involving protons and neutrons and the only difference would be the phase space in which the mass of the electron would play a small role? So, basically, we are accounting for it in the others?

I would like to post my question in the astrophysics section of the forum, but I don't know if I am allowed to, or this is considered a bad cross-posting...