# Big Bang Nucleosynthesis

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?

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).

• I get the part where it doesn't interact using electro-magnetic forces. The part I don't get is that DM had to form out of the same radiation budget as the rest of the particles. So 80% of the photons used to created all matter had to be converted into whatever ended up as dark matter. Since the ratio of protons to neutrons is based on a statistical model, I'm completely mystified how we can draw any conclusions while missing 80% (by mass) of the reactions going on at this time. – user32023 Nov 8 '15 at 19:19
• Also, as I understand them, the LUX and $Xenon_{500}$ experiments are based on the theory that the recoil between a nucleon and a dark matter particle would release a photon. How come we don't expect a soup as dense as $100\times 10^9 K$ that fits in the size of a grapefruit to produce enough photons to change the statistics? – user32023 Nov 8 '15 at 19:25
• Dark matter does not form out of photons, since it does not interact electromagnetically. – ProfRob Nov 8 '15 at 19:26
• Does the same logic apply to neutrinos? – user32023 Nov 8 '15 at 19:27
• @DonaldRoyAirey Additional neutrino species would make a difference to BBN. That is why some things get ruled out. Dark matter would have already been present before nucleosynthesis began. Completely decoupled matter makes no difference or contribution to a statistical equilibrium calculation. – ProfRob Nov 8 '15 at 19:51

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

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

• "Presumably there are also dark matter particles, but they do not matter for BBN." Excuse me but could you please explain to me how is this science? I'm not an expert on nuclear reactions, but I'm pretty sure your statistical analysis is bogus if you ignore 80% of the reactions. – user32023 Nov 8 '15 at 16:53
• @DonaldRoyAirey Dark matter did not affect BBN, because it does not interact strongly (otherwise it would bind to atomic nuclei today and we would see heavy atoms). It might interact weakly, but very rarely. The observed abundances of isotopes in the universe meet the theoretical calculations that do not involve dark matter. If dark matter did take part in BBN, the isotope abundances would be different today. – mpv Nov 8 '15 at 21:15
• @DonaldRoyAirey : Note that BBN occurs at $kT$ in the neighborhood of a few MeV and less. If dark matter intereacted with nucleons at these low energies, we would nkow more about dark matter than we do about the Higgs because the effects would be very accessible in even small accelerators. DM decouples from electromagnetism and standard matter so much earlier in the process that it is not even an indirect participant in BBN. – Eric Towers Nov 8 '15 at 22:14
• @EricTowers - Still reading up on the subject. Apparently the term is 'Thermal Relic' meaning it came from a much hotter part of the BB than BBN. The trouble I'm having is electrons, protons, neutrons, photons and neutrinos all come from this same epoch, so I don't understand why this automatically excludes a particle from participating in a nuclear reaction. I get that they're electrically neutral, but if they're annihilating themselves at this time, why aren't the bumping into regular baryons and generating recoil photons or some other such kinetic interaction? – user32023 Nov 8 '15 at 23:11
• @mpv This logic sounds a bit like: we see no evidence of dark matter in the relative abundances of light elements, so therefore we know that DM exists. Shouldn't the fact that the nuclear reactions of BBN work only in the total absence of DM be evidence against the theory? Neutrinos are primordial relics, they are electrically neutral and regulate the production $^4He$, surely their annihilation changes the pressure, so why are we so sure that DM (which has the same attributes) plays no role? – user32023 Nov 9 '15 at 19:20

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.