Testing consistency of \(\Omega_b h^2\) in the Planck data

Abstract

We find that the cosmic microwave background temperature and polarization power spectra measurements from Planck constrain the parameter \(\Omega_bh^2\) mostly through: A) the amplitude of Thomson scattering and B) 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 \(\Omega_b h^2\) from the Planck data alone. They are consistent, showing robustness of the Planck \(\Omega_b h^2\) constraint. We can alternatively rephrase these constraints as A) the change of the Thomson scattering cross section since recombination is less than \(\sim 2\%\) and B) momentum during recombination is conserved to better than \(\sim 2\%\) by Thomson scattering. Decoupling the eight various ways in which \(\Omega_b h^2\) affects the Planck data leads to slightly higher \(H_0\) than in the standard analysis, \((69.1 \pm 1.6)\,\mathrm{km/s/Mpc}\), but the overall consistency of all \(\Omega_b h^2\) constraints does not suggest any problem with the standard cosmological model.