Which Fundamental Constants for CMB and BAO?

Abstract

We use the three-scale framework of Hu et al. to show how the Cosmic Microwave Background anisotropy spectrum depends on the fundamental constants. As expected, the spectrum depends only on \emph{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 ${\alpha }^2{m}_e/m_p$ and the proton-CDM-particle mass ratio, $m_p/\mchi$. The distance to the last-scattering surface depends on $Gm_p\mchi/\hbar c$, so published CMB observational limits on time variations of the constants implicitly assume the time-independence of this quantity, as well as assuming a flat-\lcdm~cosmological model. On the other hand, low-redshift BAO, $H_0$ and baryon-mass-fraction measurements can be combined with the \emph{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 $G\mchi^2/\hbar c$, $m_p/\mchi$ and ${\alpha }^2{m}_e/m_p$ are equal to their present values at a precision of $\sim 15\%$.

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• Bianchi type-V Transitioning model in Brans-Dicke theory with Observational Constraint
• Hubble tension as a window on the gravitation of the dark matter sector: Exploration of a family of models
• Lyra's cosmology of homogeneous and isotropic universe in Brans-Dicke theory
• Cosmological constraints from cosmic homogeneity