Impact of first-order phase transitions on dark matter production in the scotogenic model

In this work, we investigate the effects of first-order phase transitions on the singlet fermionic dark matter in the scotogenic model. It is known that this dark matter candidate tends to conflict with the relevant constraints such as the neutrino oscillation data and charged lepton flavor violating processes if its thermal production mechanism is assumed. We find that the dark matter production mechanisms are modified by first-order phase transitions at some specific parameter regions, where the phase transitions can be one-step or two-step depending on the parameters. If the phase transition is one-step, a sufficiently low nucleation temperature is required to reproduce the observed relic abundance of dark matter. If the phase transition is two-step, the dark matter should never be thermalized, otherwise the abundance would remain too much and overclose the universe. This is because the nucleation temperature cannot be low as in the one-step case. Therefore we require another way of dark matter production, the freeze-in mechanism for the two-step case. We show that the freeze-in mechanism is modified by the temporary vacuum expectation value of the inert scalar field. In both cases, the first-order phase transitions could produce observable gravitational wave spectra. In particular for the one-step phase transition, the generated gravitational waves with sizable energy density are intrinsically correlated with the dark matter production mechanism, and can be detectable by future space-based interferometers.