On the Propagation of Gravitational Waves in the Weyl Invariant Theory of Gravity

We revisit Weyl’s unified field theory, which arose in 1918, shortly after general relativity was discovered. As is well known, in order to extend the program of the geometrization of physics started by Einstein to include the electromagnetic field, H. Weyl developed a new geometry which constitutes a kind of generalization of Riemannian geometry. In this paper, our aim is to discuss Weyl’s proposal anew and examine its consistency and completeness as a physical theory. We propose new directions and possible conceptual changes in the original work. Among these, we investigate with some detail the propagation of gravitational waves, and the new features arising in this recent modified gravity theory, in which the presence of a massive vector field appears somewhat unexpectedly. We also speculate whether the results could be examined in the context of primordial gravitational waves.