  In this paper we present a novel mechanism for producing the observed Dark
Matter(DM) relic abundance during the First Order Phase Transition (FOPT) in
the early universe. We show that the bubble expansion with ultra-relativistic
velocities can lead to the abundance of DM particles with masses much larger
than the scale of the transition. We study this non-thermal production
mechanism in the context of a generic phase transition and the electroweak
phase transition. The application of the mechanism to the Higgs portal DM as
well as the signal in the Stochastic Gravitational Background are discussed.
