  We analyse six classes of t-channel dark matter simplified models in which
the Standard Model field content is extended by a coloured mediator and a dark
matter state. The two new states are enforced to be odd under a new parity,
while all Standard Model fields are taken even so that dark matter stability is
guaranteed. We study several possibilities for the spin of the new particles
and the self-conjugate property of the dark matter, and we focus on model
configurations in which the dark matter couples to the right-handed up quark
for simplicity. We investigate how the parameter spaces of the six models can
be constrained by current and future cosmological, astrophysical and collider
searches, and we highlight the strong complementary between those probes. Our
results demonstrate that scenarios featuring a complex (non self-conjugate)
dark matter field are excluded by cosmology and astrophysics alone, the only
possibility to avoid these bounds being to invoke very weak couplings and
mechanisms such as conversion-driven freeze-out. For models with self-conjugate
dark matter, mediator and dark matter masses are pushed deep into the TeV
regime, with the lower limits on the mediator mass reaching 3 to 4 TeV and
those on the dark matter mass 1 to 2 TeV. In large parts of the parameter space
these strong bounds are driven by same-sign mediator pair production, a channel
so far not considered in the experimental analyses embedding t-channel dark
matter model interpretations.
