Andre Wehner

Advances in Conformal Gravity

We develop an alternative spacetime gauge theory of the conformal group, which solves many of the problems typically associated with scale invariance. First, in contrast to standard conformal gauge theories, the gauge fields corresponding to special conformal transformations cannot be removed. Second, the Weyl vector is no longer necessarily coupled to unphysical phenomena. Third, this new class of "biconformal geometries" resolves the problem of writing scale-invariant vacuum gravitational actions in arbitrary dimension without the use of compensating fields. We wrote the most general linear vacuum action and solved the resulting field equations subject only to a minimal torsion assumption. We found that all such solutions were foliated by equivalent n-dimensional Ricci-flat Riemannian spacetimes.

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