Exceptional Composite Dark Matter
  We study the dark matter phenomenology of non-minimal composite Higgs models
with $SO(7)$ broken to the exceptional group $G_2$. In addition to the Higgs,
three pseudo-Nambu-Goldstone bosons arise, one of which is electrically
neutral. A parity symmetry is enough to ensure this resonance is stable. In
fact, if the breaking of the Goldstone symmetry is driven by the fermion
sector, this $\mathbb{Z}_2$ symmetry is automatically unbroken in the
electroweak phase. In this case, the relic density, as well as the expected
indirect, direct and collider signals are then uniquely determined by the value
of the compositeness scale, $f$. Current experimental bounds allow to account
for a large fraction of the dark matter of the Universe if the dark matter
particle is part of an electroweak triplet. The totality of the relic abundance
can be accommodated if instead this particle is a composite singlet. In both
cases, the scale $f$ and the dark matter mass are of the order of a few TeV.
