A note on noncompact and nonmetricit quadratic curvature gravity theories

Abstract

In this note, we evaluate the Weyl-invariant quadratic curvature tensors for the particular Weyl gauge field constructed in the $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. We subsequently extend the model to its higher curvature version. We also compute the Weyl-invariant extension of the topological Gauss-Bonnet term for this specific choice of vector field.