Cluster baryon-fraction estimate of matter density (${\Omega }_m={\Omega }_b/f_{b,\mathrm{cluster}}$)

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.