Testing consistency of Ωbh2 in the Planck data

We find that the cosmic microwave background temperature and polarization power spectra measurements from Planck constrain the parameter Ω_bh² mostly through (i) the amplitude of Thomson scattering and (ii) a factor that ensures Thomson scattering does not violate momentum conservation of the baryon-photon fluid. This allows us to obtain two distinct but comparably strong constraints on Ω_bh² from the Planck data alone. They are consistent, showing robustness of the Planck Ω_bh² constraint. We can alternatively rephrase these constraints as (i) the change of the Thomson scattering cross section since recombination is less than ∼2 % and (ii) momentum during recombination is conserved to better than ∼2 % by Thomson scattering. Decoupling the eight various ways in which Ω_bh² affects the Planck data leads to H₀ only slightly higher than in the standard analysis, (68.3 ±1.6 ) km /s /Mpc . The overall consistency of all Ω_bh² constraints does not suggest any problem with the standard cosmological model.