Mapping Poincaré gauge cosmology to Horndeski theory for emergent dark energy

The ten-parameter, quadratic Poincaré 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 noncanonical biscalar-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 noncanonical term reduces to a Cuscuton field of the form √|Xϕϕ|. 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-renormalizable cases of Poincaré gauge theory. These theories support the concordance Λ CDM background cosmology up to an optional, effective dark radiation component, we explain this behavior 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 Λ CDM.