Compactifications of conformal gravity

TL;DR

This paper demonstrates that compactifying higher-dimensional conformal gravity naturally produces Einstein gravity in lower dimensions, with the radion field acting as the scalar compensator and ensuring automatic stabilization of extra dimensions.

Contribution

It shows that extra-dimensional compactification in conformal gravity obviates the need for a scalar compensator, with the radion field fulfilling this role and stabilizing the extra dimensions.

Findings

Compactification yields Einstein gravity without scalar compensator.

Radion acts as the scalar compensator in 4D.

Size stabilization of extra dimensions is automatic.

Abstract

We study conformal theories of gravity, i.e. those whose action is invariant under the local transformation g_{\mu\nu} -> \omega^2 (x) g_{\mu\nu}. As is well known, in order to obtain Einstein gravity in 4D it is necessary to introduce a scalar compensator with a VEV that spontaneously breaks the conformal invariance and generates the Planck mass. We show that the compactification of extra dimensions in a higher dimensional conformal theory of gravity also yields Einstein gravity in lower dimensions, without the need to introduce the scalar compensator. It is the field associated with the size of the extra dimensions (the radion) who takes the role of the scalar compensator in 4D. The radion has in this case no physical excitations since they are gauged away in the Einstein frame for the metric. In these models the stabilization of the size of the extra dimensions is therefore automatic.