  We consider classically scale-invariant extensions of the Standard Model (CSI
ESM) which stabilise the Higgs potential and have good dark matter candidates.
In this framework all mass scales, including electroweak and dark matter
masses, are generated dynamically and have a common origin. We consider Abelian
and non-Abelian hidden sectors portally coupled to the SM with and without a
real singlet scalar. We perform a careful analysis of RG running to determine
regions in the parameter space where the SM Higgs vacuum is stabilised. After
combining this with the LHC Higgs constraints, in models without a singlet,
none of the regained parameter space in Abelian ESMs, and only a small section
in the non-Abelian ESM survives. However, in all singlet-extended models we
find that the Higgs vacuum can be stabilised in all of the parameter space
consistent with the LHC constraints. These models naturally contain two dark
matter candidates: the real singlet and the dark gauge boson in non-Abelian
models. We determine the viable range of parameters in the CSI ESM framework by
computing the relic abundance, imposing direct detection constraints and
combining with the LHC Higgs constraints. In addition to being instrumental in
Higgs stabilisation, we find that the singlet component is required to explain
the observed dark matter density.
