Cosmic baryon fraction ($f_b={\Omega }_b/{\Omega }_m$)

The cosmic baryon fraction is the ratio of mean baryonic matter density to total matter density. Assigning this fraction to a halo is a simplifying assumption; cooling, ejection and other baryonic processes can change the halo's retained gas and stellar fractions. A baryon conversion efficiency becomes a stellar-to-total-halo mass ratio only after multiplying by the applicable baryon fraction.

If a measured cluster baryon fraction represents the cosmic baryon fraction ${\Omega }_b/{\Omega }_m$, combining it with the cosmological baryon density inferred from Big Bang nucleosynthesis gives the displayed estimate. Gas and stellar baryons must both be counted, and all distance or Hubble constant dependence must be consistent. Baryon depletion or feedback modifies the identification: with $f_{b,\mathrm{cluster}}=b{\Omega }_b/{\Omega }_m$, the corrected answer is ${\Omega }_m=b{\Omega }_b/f_{b,\mathrm{cluster}}$. The method measures total matter rather than vacuum or radiation density.