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 ${\Omega }_b{h}^2$ 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 $H_0$ only slightly higher than in the standard analysis, $(68.3\pm 1.6)km/s/Mpc$. The overall consistency of all ${\Omega }_b{h}^2$ constraints does not suggest any problem with the standard cosmological model.

7 pages, 4 figures. Accepted version + added missing reference