Mapping Poincaré gauge cosmology to Horndeski theory for emergent dark energy

Abstract

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 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 $\sqrt{|X^{\varphi \varphi }|}$. 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 Poincaré 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.

arXiv comment11 pages, 2 figures. Results previously presented at DAMTP on 14/02/20. Added substantial introduction to Poincaré gauge theory and its perturbative renormalisability. Added various references. Incorporated supplemental material into main text (previously hosted on GitHub). Titular change. Results unaffected. Accepted for publication by Phys. Rev. D

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