Updated fundamental constant constraints from Planck 2018 data and possible relations to the Hubble tension

Abstract

We present updated constraints on the variation of the fine structure constant, ${\alpha }_{\mathrm{EM}}$, and effective electron rest mass, $m_{\mathrm{e}}$, during the cosmological recombination era. These two fundamental constants directly affect the ionization history at redshift $z\simeq 1100$ and thus modify the temperature and polarisation anisotropies of the cosmic microwave background (CMB) measured precisely with {\it Planck }. The constraints on ${\alpha }_{\mathrm{EM}}$ tighten slightly due to improved {\it Planck} 2018 polarisation data but otherwise remain similar to previous CMB analysis. However, a comparison with the 2015 constraints reveals a mildly discordant behaviour for $m_{\mathrm{e}}$, which from CMB data alone is found below its local value. Adding baryon acoustic oscillation data brings $m_{\mathrm{e}}$ back to the fiducial value, $m_{\mathrm{e}}=(1.0078\pm 0.0067)m_{\mathrm{e},0}$, and also drives the Hubble parameter to $H_0=69.1\pm 1.2$ [in units of $\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$]. Further adding supernova data yields $m_{\mathrm{e}}=(1.0190\pm 0.0055)m_{\mathrm{e},0}$ with $H_0=71.24\pm 0.96$. We perform several comparative analyses using the latest cosmological recombination calculations to further understand the various effects. Our results indicate that a single-parameter extension allowing for a slightly increased value of $m_{\mathrm{e}}$ ($\simeq 3.5\sigma$ above $m_{\mathrm{e},0}$) could play a role in the Hubble tension.

arXiv comment8 pages, 8 figures, 4 tables; modified to copy the accepted MNRAS version

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