  If the mass of dark matter is generated from a cosmological phase transition
involving the nucleation of bubbles, the corresponding bubble walls can filter
out dark matter particles during the phase transition. Only particles with
sufficient momentum to overcome their mass inside the bubbles can pass through
the walls. As a result, the dark matter number density after the phase
transition has a suppression factor $\exp(-M_\chi/2\tilde \gamma T)$, where
$M_\chi$ is the dark matter mass, and $\tilde \gamma$ and $T$ are the Lorentz
factor and temperature of the incoming fluid in the bubble wall rest frame,
respectively. Under certain assumptions, we show that the filtering-out process
can naturally provide a large suppression consistent with the observed dark
matter density for a wide range of dark matter masses up to the Planck scale.
Since the first-order phase transition is the decisive ingredient in our
mechanism, a new connection is made between heavy dark matter scenarios and
gravitational wave observations.
