Which fundamental constants for cosmic microwave background and baryon-acoustic oscillation?

IRFU-SPP, CEA Saclay, 91191 Gif-sur-Yvette, France
e-mail: rich@hep.saclay.cea.fr

Received: 29 June 2015
Accepted: 19 October 2015

Abstract

We use the three-scale framework of Hu et al. to show how the cosmic microwave background (CMB) anisotropy spectrum depends on the fundamental constants. As expected, the spectrum depends only on dimensionless combinations of the constants, and we emphasize the points that make this generally true for cosmological observables. Our analysis suggests that the CMB spectrum shape is mostly determined by α²m_e/m_p and by m_p/m_χ, the proton-CDM-particle mass ratio. The distance to the last-scattering surface depends on Gm_pm_χ/ ħc, so published CMB observational limits on time variations of the constants implicitly assume the time independence of this quantity, as well as a flat-ΛCDM cosmological model. On the other hand, low-redshift baryon-acoustic oscillation, H₀, and baryon-mass-fraction measurements can be combined with the shape of the CMB spectrum to give information that is largely independent of these assumptions. In particular, we show that the pre-recombination values of Gm²_χ/ħc, m_p/m_χ, and α²m_e/m_p are equal to their present values at a precision of ~15%.