Testing consistency of Ωbh2 in the Planck data

Abstract

We find that the cosmic microwave background temperature and polarization power spectra measurements from Planck constrain the parameter ${\mathrm{\ensuremath{\Omega}}}_{b}{h}^{2}$ 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 ${\mathrm{\ensuremath{\Omega}}}_{b}{h}^{2}$ from the Planck data alone. They are consistent, showing robustness of the Planck ${\mathrm{\ensuremath{\Omega}}}_{b}{h}^{2}$ constraint. We can alternatively rephrase these constraints as (i) the change of the Thomson scattering cross section since recombination is less than $\ensuremath{\sim}2%$ and (ii) momentum during recombination is conserved to better than $\ensuremath{\sim}2%$ by Thomson scattering. Decoupling the eight various ways in which ${\mathrm{\ensuremath{\Omega}}}_{b}{h}^{2}$ affects the Planck data leads to ${H}_{0}$ only slightly higher than in the standard analysis, $(68.3\ifmmode\pm\else\textpm\fi{}1.6)\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$. The overall consistency of all ${\mathrm{\ensuremath{\Omega}}}_{b}{h}^{2}$ constraints does not suggest any problem with the standard cosmological model.