Resolving the Hubble tension in a U(1)Lμ-Lτ model with the Majoron

We explore the possibility of resolving the Hubble tension and (g - 2)(mu) anomaly simultaneously in a U(1)(L mu-L tau) model with Majoron. We only focus on the case where the Majoron phi does not exist at the beginning of the universe and is created by neutrino inverse decay vv -> phi after electron-positron annihilation. In this case, the contributions of the new gauge boson Z' and the Majoron phi to the effective number of neutrino species N-eff can be calculated in separate periods. These contributions are labelled N-eff for the U(1)(L mu-L tau) gauge boson and Delta N-eff' for the Majoron. The effective number N-eff = N-eff' + Delta N-eff' is evaluated by the evolution equations of the temperatures and the chemical potentials of light particles in each period. As a result, we find that the heavier Z' mass m(Z') results in a smaller N-eff' and requires a larger Delta N-eff' to resolve the Hubble tension. Therefore, compared to previous studies, the parameter region where the Hubble tension can be resolved is slightly shifted toward the larger value of m(Z').

Automated summary

The study suggests that in the U(1)(L mu-L tau) model, a heavier Z' boson mass results in a smaller N-eff' and requires a larger Delta N-eff' to resolve the Hubble tension.