Spontaneous "Scalar-Vector Galileons" from "Weyl bi-Connection" model

Weyl bi-connection model manifests a natural framework to automatically produce the Galileon structure. It is shown that this framework can explain scalar Galileon, vector Galileon as well as their interactions by generalizing the Weyl non-metricity. So it can be interpreted as a geometrical realization for Galileons. The non-metricity part enjoys a $U(1)$ gauge invariance. The result is interestingly non-trivial since the Galileon structure appears spontaneously and not by demanding the absence of the Ostrogradsky ghost. This fact suggests a possible deeper conceptual relation between Weyl bi-connection model and the absence of Ostrogradsky ghost.