What It Takes to Solve the Hubble Tension through Modifications of Cosmological Recombination

Abstract

We construct data-driven solutions to the Hubble tension which are perturbative modifications to the fiducial ΛCDM cosmology, using the Fisher bias formalism. Taking as proof of principle the case of a time-varying electron mass and fine structure constant, and focusing first on Planck CMB data, we demonstrate that a modified recombination can solve the Hubble tension and lower S8 to match weak lensing measurements. Once baryonic acoustic oscillation and uncalibrated supernovae data are included, however, it is not possible to fully solve the tension with perturbative modifications to recombination.