  Dark matter that was once in thermal equilibrium with the Standard Model is
generally prohibited from obtaining all of its mass from the electroweak phase
transition. This implies a new scale of physics and mediator particles to
facilitate dark matter annihilation. In this work, we focus on dark matter that
annihilates through a generic Higgs portal. We show how partial wave unitarity
places an upper bound on the mass of the mediator (or dark) Higgs when its mass
is increased to be the largest scale in the effective theory. For models where
the dark matter annihilates via fermion exchange, an upper bound is generated
when unitarity breaks down around 8.5 TeV. Models where the dark matter
annihilates via fermion and higgs boson exchange push the bound to 45.5 TeV. We
also show that if dark matter obtains all of its mass from a new symmetry
breaking scale that scale is also constrained. We improve these constraints by
requiring perturbativity in the Higgs sector up to each unitarity bound. In
this limit, the bounds on the dark symmetry breaking vev and the dark Higgs
mass are now 2.4 and 3 TeV, respectively, when the dark matter annihilates via
fermion exchange. When dark matter annihilates via fermion and higgs boson
exchange, the bounds are now 12 and 14.2 TeV, respectively. The available
parameter space for Higgs portal dark matter annihilation is outlined. We also
show how the bounds are improved if Higgs portal dark matter is only a fraction
of the observed relic abundance. Finally, we discuss how to apply these
arguments to other dark matter scenarios and discuss prospects for direct
detection and future collider searches. If the Higgs portal is responsible for
dark matter annihilation, planned direct detection experiments will cover
almost all the parameter space. The ILC and/or VLHC, however, is needed to
establish the Higgs portal mechanism.
