Big Bang Nucleosynthesis

Question

In the very early universe, the hot plasma consisted of fixed amount of radiation (photons and neutrinos) and matter (electrons, protons, neutrons, etc). There were many competing reaction taking place and using statistical methods I understand that you can deduce the particle content of the universe when radiation and particles began to condense into nucleons (at roughly $100\times 10^9 K$).

According to ΛCDM, there is 5 times more dark matter than normal matter. These particles, ostensibly, had to form from the same budget of radiation yet I don’t see the reactions in any of the literature. How is it possible to accurately calculate the particle content of the early universe, specifically the proton to neutron ratio, when the reaction governing 80% of the matter creation isn’t known?

Answer 1

Standard big bang nucleosynthesis only involves particles which are part of the standard model - ie. excludes dark matter.

Is this justified? Well, dark matter is non-interacting (or so weakly interacting that we can't detect it), therefore it does not interact strongly with baryons and photons during the epoch of nucleon formation.

However there certainly is theoretical work that investigates non-standard big bang models that do include additional degrees of freedom due to new neutrino species or that include residual annihilation of weak scale massive dark matter particles. Apparently, these pieces of new physics have a significant effect on the nucleosynthesis of the light elements - deuterium, tritium, lithium. A reasonable review (I have not read it) appears to be given by Jedamzik & Pospelov (2009).

Some of these ideas have been used to suggest a solution to the problem that standard big bang nucleosynthesis appears to give too much Li (e.g. Bailly 2011).

Answer 2

This answer is based on David H. Weinberg from Ohio State University:

When the universe is about one second old, the particle species present are photons, neutrinos, and (at an abundance smaller by a factor ∼ $10^9$ ) protons, neutrons, and electrons. Presumably there are also dark matter particles, but they do not matter for BBN. The universe is still dense and hot enough that weak interactions involving neutrinos can convert neutrons to protons and vice versa. Since neutrons are more massive than protons, they are less abundant — conversion of a neutron to a proton is less probable than conversion of a proton to a neutron. In thermal equilibrium

$\frac{n_n}{n_p} = e^{-Q/kT} , Q \equiv (m_n - m_p) c^2 = 1.2934 MeV $

The conversion reactions become slow compared to the age of the universe at t ∼ 3 seconds, kT ∼ 0.7 MeV. Since the interaction rate is dropping quickly as the density and temperature of the universe decline, there are no subsequent conversions. The neutron-to-proton ratio “freezes in” at

$\frac{n_n}{n_p} = e ^{-1.2934/0.7} = 1/6$

Answer 3

I've made a verbose answer to you other question, but I believe it is as much relevant here: https://physics.stackexchange.com/a/259646/119172

From the comments on this page, I see many assumptions regarding the nature of dark matter which confuse the whole story. First, you need to understand that dark matter is a phenomenon. It is combination of matter deficiencies in many cases (e.g., see this: http://sciencewise.info/definitions/Dark_matter_by_Oleg_Ruchayskiy). Everything suggests that this is a particle (as opposed to another phenomenon, dark energy that cannot be a particle because it is constant in space), but we do not know yet it's properties.

But, since we still haven't found it, it has to hide from us very hard. This is the basic point that allows to exclude dark matter from consideration of BBN. All we need to assume is that it is long-lived and interacts mostly gravitationally. Everything else is negligible in cosmological point view.

But there's a lot of dark matter, isn't there? Yes, estimated energy content of dark matter is much more than one of the matter or radiation. But this wasn't always the case. Different kinds of matter take turns dominating the Universe because their energy fractions evolve (see, e.g., https://www.wikiwand.com/en/Friedmann_equations#/Density_parameter).

So, if dark matter is a particle, then during BBN it would either be unimportant if it is heavy (because then Universe is dominated by radiation) or will constitute yet another ultra-relativistic component of the plasma. And our cosmological measurements nowadays has a margin of error precisely for one more ultra-relativistic specie.