Scale invariant Einstein-Cartan gravity and flat space conformal symmetry

TL;DR

This paper explores conditions where scale-invariant Einstein-Cartan gravity with scalar fields approximates conformal symmetry at high energies, introducing a minimal model with a massless dilaton that could unify gravity and particle physics.

Contribution

It identifies conditions for approximate conformal invariance in Einstein-Cartan gravity with scalar matter, proposing a minimal model including a massless dilaton that extends Standard Model physics.

Findings

Models can be approximately conformally invariant up to the Planck scale.

Minimal models include only a massless dilaton besides Standard Model fields and graviton.

Predictions are similar to Higgs-inflation scenarios.

Abstract

We find the conditions under which scale-invariant Einstein-Cartan gravity with scalar matter fields leads to an approximate conformal invariance of the flat space particle theory up to energies of the order of the Planck mass. In the minimal setup, these models, in addition to the fields of the Standard Model and the graviton, contain only one extra particle -- a massless dilaton. Theories of this type can pave the way for a self-completion all the way up the Planck scale and lead to rather universal inflationary predictions, close to those of the simplest Higgs-inflation scenario in the metric theory of gravity.