In Big Bang Nucleosynthesis (BBN), why aren't anti-protons created and destroyed?

I'm working through BBN theory with Dodelson and other papers. I have a question about the reactions between particles in the $$1\space MeV$$ range. We have reactions that produce and annihilate protons and neutrons during this epoch, so where is the treatment for anti-protons and anti-neutrons? Isn't the universe creating and destroying anti-protons and anti-neutrons during this same time? Won't the anti-protons and protons react during this epoch to produce photons? Won't high-energy photons collide and produce protons and anti-protons?

Yes, I know about the hand-waving argument that we're just going to pretend there's some asymmetry between matter and anti-matter and jam in a free parameter which is the baryon-photon ratio at the onset of nucleosynthesis, but that doesn't address the fact that anti-protons should be created under the same conditions as protons. It appears that the abundance of any given species of particle at a given time depends on accounting for every possible reaction. I don't understand the justification for leaving out what appears to me to be the most important reaction of the $$1\space MeV$$ temperature range.

• Without access to the specific references you're working with, this question is difficult to understand. It would help if you included what reactions specifically you're talking about, and what the assumed particle content of the universe at that point in time is. – ACuriousMind Apr 11 at 15:00
• @ACuriousMind - Dodelson, Scott - Modern Cosmology Chapter 3. The universe consists of protons, electrons, positrons, neutrons and high-energy photons at this point. I don't see any discussion or consideration of anti-protons or anti-neutrons at this point, though I consider it self-evident that if protons are created in these conditions, then we should be creating anti-protons as well. The major reactions tracked during this discussion is the proton to neutron ratio and, then, ultimately, Deuterium and $^4He$ – Gluon Soup Apr 11 at 15:04

1 Answer

Anti-protons have a rest-mass energy of 938 MeV. They are not created in reactions at temperatures of just 1 MeV and neither are protons or neutrons.

The protons were created much earlier (at around $$10^{-6}$$s and $$k_BT\sim 1$$ GeV, along with anti-protons), but most of them annihilated with anti-protons as the universe cooled, leaving the protons that remain due to the baryon asymmetry, and a huge ($$\sim 10^{9}$$) excess of photons.

The proton/neutron ratio isn't changing (at $$k_BT \sim 1$$ MeV) because baryons are being created and destroyed; it changes because weak interactions are able to change neutrons to protons and vice-versa and the rest mass energy difference between a neutron and a proton is only 1.4 MeV.

• If there is no annihilation at temperatures on the order of $1\space MeV$, then what physical process is changing the ratio between protons and neutrons (in equilibrium, that is, I understand that neutrons decay once they fall out of equilibrium)? – Gluon Soup Apr 11 at 15:34
• In the absence of this mysterious baryon asymmetry, is there an expectation that an equal number of baryons and photons would exist? I understand that protons and anti-protons annihilate and produce photons, but is there a baseline to say "this is what the baryon-photon ratio would be without the reaction of protons and anti-protons"? – Gluon Soup Apr 11 at 15:59
• @GluonSoup No, the expectation is that all the baryons would annihilate and the universe would be full of photons, since they are not energetic enough to produce massive particles once $T<$ a few hundred MeV. – ProfRob Apr 11 at 16:00