Constraints on new physics around the MeV scale with cosmological observations

We investigate the joint effect of the cosmological phase transitions, thermal light dark matter, and the lepton asymmetry on the big bang nucleosynthesis and cosmic microwave background. We find that all of them can modify the predictions of the effective number of neutrino species and primordial nucleosynthesis. In turn, we observe that: 1) the cosmological observations can exclude slow and strong phase transitions with strength even smaller than $\mathcal{O}(10^{-3}-10^{-2})$; 2) a much larger portion of dark matter mass region is excluded when the phase transition temperature is closer to 1 MeV; and 3) the magnitude of the non-vanishing neutrino lepton asymmetry is limited to be around $\mathcal{O}(10^{-2}-10^{-1})$ depending on the phase transition strength. These phase transitions can produce stochastic gravitational wave background to be probed by pulsar timing array experiments.