The mass effect -- Variations of the electron mass and their impact on cosmology

We summarize and explain the current status of time variations of the electron mass in cosmology, showing that such variations allow for significant easing of the Hubble tension, from the current $\sim 5\sigma$ significance, down to between $3.4\sigma$ and $1.0\sigma$ significance, depending on the precise model and data. Electron mass variations are preferred by Cosmic Microwave Background (CMB) data in combination with the latest results on baryonic acoustic oscillations (BAO) and type Ia supernovae at a level of significance between $2\sigma$ and $3.6\sigma$ depending on the model and the data. This preference for a model involving an electron mass variation is neither tightly constrained from light element abundances generated during big bang nucleosynthesis nor from post-recombination observations using quasars and atomic clocks, though future data is expected to give strong evidence in favor of or against this model.