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Einstein-Cartan gravity goes HD!

May. 09, 2022

Gravity can appear in many incarnations, including not only the most common metric approach but also the Palatini, teleparallel, and Einstein-Cartan formulations. These realizations differ mainly in their choice of fundamental degrees of freedom, being otherwise mathematically equivalent as pure gravity is concerned. The degeneracy among different realisations breaks down, however, in the presence of non-minimal couplings to matter, as happens unavoidably when accounting for the Standard Model Higgs.

In a recently published article in the Journal of Cosmology and Astroparticle Physics, the COSTAR members Matteo Piani and Javier Rubio, studied the inflationary predictions of the Higgs-Dilaton (HD) model in Einstein-Cartan gravity. By focusing on the separate impact of the Holst and Nieh-Yan terms on the inflationary observables, and using analytical and numerical techniques, they showed that the predictions of these scenarios display an attractor-like behaviour intrinsically related to the curvature of the field-space manifold in the metric formulation of the theory. Beyond that, the analysis of the Nieh-Yan case revealed also the existence of an additional attractor solution induced by a cubic pole in the inflaton kinetic term that becomes relevant at large dilaton couplings. This constitutes a unique feature of the Einstein-Cartan formulation as compared to the more renowned metric and Palatini counterparts.