Big bang nucleosynthesis constraints on varying electron mass solution to the Hubble tension

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A cosmological model with a time-varying mass of electrons seems a promising solution for the so-called Hubble tension. We examine the big bang nucleosynthesis (BBN) constraints on the time-varying electron mass model, because a larger electron mass gives rise to the smaller neutron decay rate which could affect the light element abundance. Additionally, different inferred cosmological parameters, primarily baryon asymmetry, to keep the cosmic background power spectrum unchanged could affect the abundance of light element. We find that the predicted helium fraction becomes larger and the deuterium abundance becomes smaller as the electron mass at the BBN time becomes larger. Thus, we conclude that an acceptable electron mass at the BBN time would be only approximately 1% greater than the current electron mass.