Q re early universe matter-antimatter annihilation

[Buzz Bloom]

I have seen several estimates that the period during the early universe in which almost all the protons, neutrons, anti-protons, and anti-neutrons (P, N , AP, AN) were annihilated occurred about 1 second after the big bang. I conceptualize this as a period in which as the temperature cooled fewer new pairs were created than the pairs that annihilated themselves until no AP and AN were left.

My question is:

Do any of the participants here at the PF know of an estimate (or can suggest a reference) of the net fraction of mass (P, N , AP, and AN) that was converted to energy during this era (either directly or after further annihilations of possibly smaller particles created by P, N , AP, and AN annihilations).​

 

[PeterDonis]

Do any of the participants here at the PF know of an estimate (or can suggest a reference) of the net fraction of mass (P, N , AP, and AN) that was converted to energy during this era

Almost all of it. That is because the ratio of baryons to photons in our current universe is about $10^8$ photons for every baryon, and this ratio is unchanged from the time of baryon-antibaryon annihilation. This ratio means that for every baryon in our universe since the annihilation, $10^8$ baryon-antibaryon pairs were annihilated. So all but 1 part in $10^8$ of the mass contained in baryons before the annihilation was converted to energy.

 

[Orodruin]

mass contained in baryons before the annihilation was converted to energy.

Et tu, Brute!

 

[Buzz Bloom]

So all but 1 part in 10⁸ of the mass contained in baryons before the annihilation was converted to energy.

Hi @PeterDonis:
Does this mean that there was exactly one photon for each baryon before the annihilations? There were also electrons and positrons, right? Were there not also photons corresponding to the leptons?

Regards,
Buzz

 

[PeterDonis]

Does this mean that there was exactly one photon for each baryon before the annihilations?

No. The photons were created by the annihilations of baryons and antibaryons.

There were also electrons and positrons, right? Were there not also photons corresponding to the leptons?

Yes. A more precise calculation would include those as well. It wouldn't change the basic point I was making.

 

[Chalnoth]

Almost all of it. That is because the ratio of baryons to photons in our current universe is about $10^8$ photons for every baryon, and this ratio is unchanged from the time of baryon-antibaryon annihilation. This ratio means that for every baryon in our universe since the annihilation, $10^8$ baryon-antibaryon pairs were annihilated. So all but 1 part in $10^8$ of the mass contained in baryons before the annihilation was converted to energy.

That doesn't make much sense to me. Photon number isn't conserved, and photons are created and destroyed all the time. The number of photons in a thermal photon gas per unit volume is strictly a function of the temperature of said gas. Thus the high-energy photons that would have resulted from an annihilation would likely have the energy from those photons spread out among a much larger number of lower-energy photons.

Furthermore, baryon (proton, neutron) annihilations tend to create not two particles, but a shower of particles, as strong force interactions are very messy.

 

[PeterDonis]

That doesn't make much sense to me.

I agree it's not a rigorous demonstration of how many photons were in the universe over time. But I think it's a fair heuristic for answering the OP's question, how much of the mass contained in baryons/antibaryons in the early universe was converted to energy.

The number of photons in a thermal photon gas per unit volume is strictly a function of the temperature of said gas.

I don't think this takes into account the expansion of the universe. In an expanding universe, I think photon number density can be constant while the temperature decreases, because the photons are redshifted by the expansion. But this is just heuristic; I have not looked at the math.

baryon (proton, neutron) annihilations tend to create not two particles, but a shower of particles, as strong force interactions are very messy.

This is true, but I'm not sure it makes much difference if all we want is an approximate answer to the OP's question, because the shower of particles ends up being converted (mostly) to photons eventually, through subsequent reactions.

I'll see if I can find a reference that goes into this in more detail.

 

[Chalnoth]

I don't think this takes into account the expansion of the universe. In an expanding universe, I think photon number density can be constant while the temperature decreases, because the photons are redshifted by the expansion. But this is just heuristic; I have not looked at the math.

The number density drops with the expansion. The number of photons per comoving volume stays the same, but the comoving volume increases in size.

Also, just fyi, photon number density scales as $T^3$, so the gas stays thermal during the expansion.

This is true, but I'm not sure it makes much difference if all we want is an approximate answer to the OP's question, because the shower of particles ends up being converted (mostly) to photons eventually, through subsequent reactions.

I'll see if I can find a reference that goes into this in more detail.

These calculations can usually be found under the topic of baryogensis:
https://en.wikipedia.org/wiki/Baryogenesis

The short of it is that there's some reasonably complicated thermodynamic arguments that go into it.

 

[PeterDonis]

These calculations can usually be found under the topic of baryogensis:
https://en.wikipedia.org/wiki/Baryogenesis

The short of it is that there's some reasonably complicated thermodynamic arguments that go into it.

Ah, so this article says a better parameter is the entropy density, which stays the same (to a good approximation) as the universe expands. And at present, the entropy density is of the same order of magnitude as the photon density (7.04 times the photon density, according to the article), so the heuristic I gave actually works OK, but only by coincidence (since the ratio of entropy density to photon density will change with time). But the correct heuristic is that the ratio of entropy density to baryon density is very large (about a billion to one, roughly, based on the numbers in the article), indicating that almost all of the baryon-antibaryon pairs in the early universe annihilated.