Questions re: Matter-Antimatter Annihilation

[Buzz Bloom]

I am having trouble getting my head around several of the concepts related to the very early activities of the universe expansion. For this thread in particular, what are the assumptions regarding the relative number of particles of different species before and after annihilation.

First, I am aware that the nucleon antinucleon annihilation occurred much before the electron positron annihilation.

1. Was is the assumed ratio r_p of the number of per unit volume (PUV) of protons before to after their annihilation with antiprotons?

2. Was is the assumed ratio r_e of the number of PUV of electrons before to after their annihilation with positrons?

I am concluding that there must be an assumed value for this 2nd ratio because of the calculation of the temperature difference between photons and neutrinos. The temperature difference would be the difference in average kinetic energy of the various particles in equilibrium with the photons due to the energy released by the annihilation.

I am assuming that the number n_pa of protons PUV after annihilation is the same as the number n_ea of electrons PUV after annihilation, because the net charge of the universe is supposed to be zero. However, these two values before annihilation, n_pb and n_eb, need not necessarily be the same. If

r_p = r_e​

then

n_pb = n_eb.​

3. If these equalities are assumed to hold, what is the justification for this assumption?

 

[Chalnoth]

These ratios are a bit difficult to quantify, because they depend upon temperature. One way of thinking of it is that there is a number of protons around that represents the matter/anti-matter imbalance plus a bunch of proton/anti-proton pairs that are there due to the high temperature. At higher temperatures, there are more proton/anti-proton pairs.

With the electrons, a similar dynamic is occurring, but because the electrons have a much lower mass (about 1/2000th the mass of the proton), there are a much larger number of thermally-produced electron/positron pairs at the same temperature. To add even more complexity to the whole mess, at these high temperatures the protons are converting to/from neutrons by interacting with electrons and neutrinos.

Overall, it's very possible to calculate based upon known physics the number density of all of these components (protons, anti-protons, neutrons, anti-neutrons, electrons, positrons, etc.). The only necessary observable inputs are the normal and dark matter densities today. From there it's just a matter of doing some fairly complicated calculations to determine the densities of these various components at different points in time.

 

[Buzz Bloom]

From there it's just a matter of doing some fairly complicated calculations to determine the densities of these various components at different points in time.

Hi @Chalnoth:

Thanks for your post.

Can you suggest a reference that gives the results of these calculations for some assumed values for the relevant variables, such as temperature and densities. Or alternatively a reference that gives the equations and explains how to do the calculations.

Regards,
Buzz

 

[Chronos]

The ratio of anti matter to matter in the early universe is believed to be about 1 part per billion matter excess based on photon abundance. See http://scienceline.ucsb.edu/getkey.php?key=114 for further discussion.

 

[Buzz Bloom]

The ratio of anti matter to matter in the early universe is believed to be about 1 part per billion matter excess based on photon abundance.

Hi @Chronos:

This was exactly the kind of help I was looking for. Your answer and the link are great. But, as I anticipated, the answer leads to another question that I find much more interesting.

Here is a quote from the link.

It turns out that the laws of nature don't obey the symmetries mentioned above exactly. They almost do. Experiments, for instance, show that a certain type of decay of long-lived kaons produce 301 positron for every 299 electrons. If the symmetries were exact, the decays should have produced 300 positrons and 300 electrons. As the universe evolved after the Big Bang, these very small symmetry violations may have resulted in the abundance of matter and the dearth of antimatter we see today.​

If I am correctly interpret the quote from your post and the quote from the link, there seems to be a very strange coincidence. I would very much appreciate a correction to my interpretation that avoids this strangeness.

First, the example in the quote above is in the wrong direction. There should be a net excess of electrons, not of positrons. The quote suggests there are many such reactions that have similar asymmetries, and when all are combined, there would be a be a net surplus of electrons. For the purpose of this post, I am going to take into account a quote from Chalnoth's post:

because the electrons have a much lower mass (about 1/2000th the mass of the proton), there are a much larger number of thermally-produced electron/positron pairs at the same temperature.

Now here is the more interesting issue.

The ratio r_p of the proton count density before to after annihilation is about a billion, while the ratio r_e of the electron count density before to after annihilation (in my assumed example) is only about 150. It seems oddly and extremely coincidental that these random asymmetrical processes could result in a net zero charge in the universe. A random asymmetric process creates (about) 2,000,000,001 protons and 1,999,999,999 anti-protons up until the time when annihilation occurs, and a combination of other random asymmetric processes creates (about) 4,000,000,000,001 electrons and 3,999,999,999,999 positrons. So what happens? These two random processes by some strange unknown mechanism turns out to produce after annihilation exactly the same numerical density value for protons and electrons.

Regards,
Buzz

 

[Chronos]

This http://hyperphysics.phy-astr.gsu.edu/hbase/astro/wcep.html may be helpful. While it may not adequately address all your questions it appears to cover the basics. The basic question is by no means completely solved, but, we have strong evidence the universe as a whole is electrically neutral. In a charged universe, gravity would not dominate in the way suggested by modern observational evidence. So, we can be confident the answer to the question is the universe is electrically neutral. But, as usual, the devil is in the details. The why part is still a work in progress.

 

[PeterDonis]

The quote suggests there are many such reactions that have similar asymmetries, and when all are combined, there would be a be a net surplus of electrons.

More precisely, when all of the reactions that actually took place in the early universe are combined, there would be a net surplus of electrons. I don't think it's assumed that every single reaction that is possible according to theory made a significant contribution in the early universe.

 

[Buzz Bloom]

While it may not adequately address all your questions it appears to cover the basics.

Hi @Chronos:

Thanks very much for your post, especially the link.

If I interpret the link correctly, the following quote from the link seems to agree with my conclusion that the explanation for why the universe is electrical neutral is still a mystery.

So there had to be some asymmetry which left us with a remnant population of electrons, and just the right number of electrons to give us an electrically neutral universe where gravity is dominant. This classic problem is often called the matter-antimatter problem, and we have some tentative suggestions about how the asymmetry came about.​

As I interpret this, it says that current physics has ideas about mechanisms for asymmetry that resulted in a surplus of electrons, but there are no ideas mentioned about why this surplus exactly matches the proton surplus.

BTW, I started another thread to discuss that particular mystery:

https://www.physicsforums.com/threads/why-does-the-universe-have-no-net-charge.843865 .​

Regards,
Buzz

 

[Buzz Bloom]

when all of the reactions that actually took place in the early universe are combined, there would be a net surplus of electrons.

Hi Peter:

Thanks for your post. I appreciate the improved clarity in your rephrasing.

Regards,
Buzz