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Weyl bi-connection model manifests a natural framework to automaticallyproduce the Galileon structure. It is shown that this framework can explainscalar Galileon, vector Galileon as well as their interactions by generalizingthe Weyl non-metricity. So it can be interpreted as a geometrical realizationfor Galileons. The non-metricity part enjoys a $U(1)$ gauge invariance. Theresult is interestingly non-trivial since the Galileon structure appearsspontaneously and not by demanding the absence of the Ostrogradsky ghost. Thisfact suggests a possible deeper conceptual relation between Weyl bi-connectionmodel and the absence of Ostrogradsky ghost.

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