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

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 weak interaction rate for the proton and neutron conversion, which could affect the light element abundance. Additionally, different inferred cosmological parameters, primarily baryon asymmetry, keeping the cosmic microwave background power spectrum unchanged could affect the abundance of light element. We find that the resultant proton-to-neutron ratio is not so much sensitive with respect to the electron mass because the change of weak interaction rate becomes important after the cosmic temperature becomes lower than the electron mass, while the slightly smaller present Hubble parameter and the electron mass are indicated if the BBN data are taken into account. We also find that the baryon density is more stringently constrained by the baryon acoustic oscillation data rather than the BBN. We have derived the ratio of the electron mass at early Universe and the present $m_e/m_{e0}=1.0028\pm 0.0064$ and $H_0=68.0\pm 1.1\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$.

Figure 1

The suppression of $\lambda (n\to p^{+})$ for $m_e=1.03\times m_{e0}$ as a function of $T/m_{e0}$.

Figure 2

Posterior distributions of light elements abundance $Y_P$ and $D/H$, $m_e/m_{e0}$, and $H_0$ for several values of $m_e/m_{e0}$.