  First-order phase transitions exist in many models beyond the Standard Model
and can generate detectable stochastic gravitational waves for a strong one.
Using the cosmological observables in big bang nucleosynthesis and cosmic
microwave background, we derive constraints on the phase transition temperature
and strength parameter in a model-independent way. For a strong phase
transition, we find that the phase transition temperature should be above
around 2 MeV for both reheating photon and neutrino cases. For a weak one with
the temperature below 1 MeV, the phase transition strength parameter is
constrained to be smaller than around 0.1. Implications for using a first-order
phase transition to explain the NANOGrav observed gravitational wave signal are
also discussed.
