Induced Gravity I: Real Scalar Field

TL;DR

This paper demonstrates that a classically scale-invariant gravity theory with a single scalar field can produce Einstein gravity through dimensional transmutation and has an ultraviolet fixed point, though stability issues remain.

Contribution

It shows how scale-invariant gravity coupled to a scalar field can generate Einstein gravity and identifies the fixed point structure of the theory.

Findings

Dimensional transmutation leads to Einstein-Hilbert action

Existence of an ultraviolet fixed point for coupling ratios

Fixed point does not include stable transmutation regions

Abstract

We show that classically scale invariant gravity coupled to a single scalar field can undergo dimensional transmutation and generate an effective Einstein-Hilbert action for gravity, coupled to a massive dilaton. The same theory has an ultraviolet fixed point for coupling constant ratios such that all couplings are asymptotically free. However the catchment basin of this fixed point does not include regions of coupling constant parameter space compatible with locally stable dimensional transmutation. In a companion paper we will explore whether this more desirable outcome does obtain in more complicated theories with non-Abelian gauge interactions.