  We study the possibility to populate the dark sector through a phase
transition. We will consider secluded dark sectors made of gauge theories,
Randall-Sundrum scenarios and conformally coupled elementary particles. These
sectors have in common the fact that the action is approximately Weyl
invariant, implying that particle production due to time dependent background
is strongly suppressed. In particular no significant production takes place
during inflation allowing to avoid strong isocurvature constraints from CMB. As
we will show, if the scale of inflation is large compared to the dynamical mass
scale, these sectors automatically undergo a phase transition that in the
simplest cases is controlled by the Hubble parameter. If the phase transition
takes place during reheating or radiation the abundance obtained can be larger
than particle production and production from the SM plasma. For phase
transitions completing during radiation domination, the DM mass is predicted in
the range $10^8$ GeV while larger values are required for phase transitions
occurring during reheating.
