While I'm studying the baryon asymmetry, the ratio of baryons number to the photons number in the universe - some times is called baryon density - $: \eta= n_b/n_\gamma$

I have found many experimental bounds or theoretical predictions on $\eta$ (as I understood). They are:

  • First: Big Bang Nucleosynthesis (BBN) : Till my understanding this is a theory predicts $\eta$ according to the abundance of light elements in the early universe, is this right?

The recent paper I have found on how BBN predicts $\eta$ is


where $\eta$ known to be of order $6.07\pm0.33 \times 10^{-10}$, but I can't get exactly form the paper the value of $\eta$! Or from the graph figure 24.1.

  • Second: Another particle data group review :

I found this paper : https://arxiv.org/abs/2106.05338

Mentions that $\eta \approx 8.6 \pm 0.1 \times 10^{-11} $, as observed. The question here:

  • I can't find in the PDG review they cited:


the $\eta$ value they have written

  • How here $\eta$ is observed? Is that from the cosmic microwave background, same as released by Planck satellite collaboration:


But again in this release, table page 8, it's mentioned the baryon density $\sim 0.022$, is that another definition?

Any help is appreciated!


1 Answer 1


In Figure 24.1 of https://pdg.lbl.gov/2020/reviews/rpp2020-rev-bbang-nucleosynthesis.pdf they plot light element abundances as functions of baryon-to-photon ratio, according to theoretical prediction. The CMB value is vertical narrow line which is centered at around $6\times 10^{-10}$ (they use logarithmic scale). Yellow boxes are from observed light element abundances. The lithium abundance is in tension with other light element observations as well as CMB data, so they refer to it as "lithium problem".

In https://arxiv.org/abs/2106.05338 they used different baryon asymmetry parameter (baryon-to-entropy density) which I already mentioned here.

The baryon density, $\Omega_bh^2\approx 0.022$ ($h$ is a conventional normalisation parameter -- essentially dimensionless Hubble parameter), used in the Planck paper is again a different parameter. This is baryon density fraction with respect to total energy density of the Universe (which is close to one).


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