The effective inflationary potential of constant-torsion emergent gravity

Abstract

Constant-torsion emergent gravity (CTEG) has a Lagrangian quadratic in curvature and torsion, but without any Einstein-Hilbert term. CTEG is motivated by a unitary, power-counting renormalisable particle spectrum. The timelike axial torsion adopts a vacuum expectation value, and the Friedmann cosmology emerges dynamically on this torsion condensate. We show that this mechanism -and the whole background cosmology of CTEG -may be understood through the effective potential of a canonical single scalar field model. The effective potential allows for hilltop inflation in the early Universe. In the late Universe, the Hubble friction overdamps the final quadratic approach to the effective minimum at the condensate, where the value of the potential becomes the cosmological constant. We do not consider particle production through spin-torsion coupling, or running of Lagrangian parameters. The model must be completed if reheating and a separation of inflationary and dark energy scales are to be understood. It is suggested that the divergence of the potential at large values of the scalar is inconsistent with the linearised propagator analysis of CTEG around zero-torsion Minkowski spacetime. This background may therefore be a strongly coupled surface in CTEG.