Conformal and Weyl-Einstein gravity: Classical geometrodynamics

Understand

We present a new formulation for the canonical approach to conformal (Weyl-squared) gravity and its extension by the Einstein-Hilbert term and a nonminimally coupled scalar field.

• For this purpose we use a unimodular decomposition of the three-metric and introduce unimodular-conformal canonical variables.
• The important feature of this choice is that only the scale part of the three-metric and the rescaled trace part of the extrinsic curvature change under a conformal transformation.
• This significantly simplifies the constraint analysis and manifestly reveals the conformal properties of a theory that contains the conformally invariant Weyl-tensor term.