  For the first time, the expected stochastic gravitational wave background is
probably discovered after observing the Hellings Downs correlation curve by
several pulsar timing array (PTA) collaborations around the globe including
NANOGrav, European PTA, Parkes PTA, and Chinese PTA. These new observations can
help to explore or constrain the dark matter (DM) formation mechanisms in the
early Universe. We study the implication of those results on the dynamical DM
formation mechanisms through a dark first-order phase transition in the early
Universe. Both the Q-ball DM and super-cool DM are investigated in the strong
super-cooling dark phase transition scenario which may give an interpretation
of the observed stochastic gravitational wave background.
