Mapping Poincar\'{e} gauge cosmology to Horndeski theory for emergent dark energy

TL;DR

This paper maps Poincaré gauge cosmology to a bi-scalar-tensor theory, revealing novel dark energy solutions and showing compatibility with standard cosmology, thus offering a unified framework for exploring alternative gravity models.

Contribution

It introduces a metrical analogue linking Poincaré gauge theories to Horndeski-like models, enabling new insights into dark energy and cosmological solutions.

Findings

Supports ΛCDM background with dark radiation from Cuscuton behavior.

Derives dark energy solutions including accelerated expansion and emergent dark energy.

Maps various Poincaré gauge theories to known scalar-tensor frameworks.

Abstract

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.