Fourth order Weyl gravity

Abstract

The fourth order Weyl gravity theory of Mannheim and Kazanas is based on replacing the Einstein-Hilbert action with the square of the Weyl tensor, and on modifying the matter action of the standard model of particle physics to make it conformally invariant. This theory has been suggested as a model of both dark matter and dark energy. We argue that the conformal invariance is not a fundamental property of the theory, and instead is an artifact of the choice of variables used in its description. We deduce that in the limit of weak fields and slow motions the theory does not agree with the predictions of general relativity, and is therefore ruled out by Solar System observations.

reference added, minor changes

References in corpus (1)

• Light deflection in Weyl gravity: critical distances for photon paths

Cited by in corpus (4)

• General class of wormhole geometries in conformal Weyl gravity
• Schwarzschild limit of conformal gravity in the presence of macroscopic scalar fields
• X-ray clusters of galaxies in conformal gravity
• Spontaneous breaking of conformal invariance, solitons and gravitational waves in theories of conformally invariant gravitation