Impact of vacuum stability, perturbativity and XENON1T on global fits of
  $\mathbb{Z}_2$ and $\mathbb{Z}_3$ scalar singlet dark matter
  Scalar singlet dark matter is one of the simplest and most predictive
realisations of the WIMP (weakly-interacting massive particle) idea. Although
the model is constrained from all directions by the latest experimental data,
it still has viable regions of parameter space. Another compelling aspect of
scalar singlets is their ability to stabilise the electroweak vacuum. Indeed,
models of scalar dark matter are not low-energy effective theories, but can be
valid all the way to the Planck scale. Using the GAMBIT framework, we present
the first global fit to include both the low-energy experimental constraints
and the theoretical constraints from UV physics, considering models with a
scalar singlet charged under either a $\mathbb{Z}_2$ or a $\mathbb{Z}_3$
symmetry. We show that if the model is to satisfy all experimental constraints,
completely stabilise the electroweak vacuum up to high scales, and also remain
perturbative to those scales, one is driven to a relatively small region of
parameter space. This region has a Higgs-portal coupling slightly less than 1,
a dark matter mass of 1 to 2 TeV and a spin-independent nuclear scattering
cross-section around 10$^{-45}$ cm$^2$.
