Mapping Poincar\'{e} gauge cosmology to Horndeski theory for emergent
  dark energy
  The ten-parameter, quadratic Poincar\'e gauge theory of gravity is a
plausible alternative to general relativity. We show that the rich background
cosmology of the gauge theory is described by a non-canonical bi-scalar-tensor
theory in the Jordan frame: the `metrical analogue'. This provides a unified
framework for future investigation by the broader community. For many parameter
choices, the non-canonical term reduces to a Cuscuton field of the form
$\smash{\sqrt{|X^{\phi\phi}|}}$. The Einstein-Cartan-Kibble-Sciama theory maps
to a pure quadratic Cuscuton, whereas the teleparallel theory maps to the
Einstein-Hilbert Lagrangian. We apply the metrical analogue to novel unitary
and power-counting-renormalisable cases of Poincar\'e gauge theory. These
theories support the concordance $\Lambda$CDM background cosmology up to an
optional, effective dark radiation component, we explain this behaviour in
terms of a stalled Cuscuton. We also obtain two dark energy solutions from one
of these cases: accelerated expansion from a negative bare cosmological
constant whose magnitude is screened, and emergent dark energy to replace
vanishing bare cosmological constant in $\Lambda$CDM.
