  We show that a conformal-invariant dark sector, interacting conformally with
the Standard Model (SM) fields through the Higgs portal, provides a viable
framework where cold dark matter (CDM) and invisible Higgs decays can be
addressed concurrently. Conformal symmetry naturally subsumes the Z_2 symmetry
needed for stability of the CDM. It also guarantees that the weaker the
couplings of the dark sector fields to the SM Higgs field, the smaller the
masses they acquire through elektroweak breaking. The model comfortably
satisfies the bounds from Large Hadron Collider (LHC) and Planck Space
Telescope (Planck 2013).
