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Bi-Connected Gauss-Bonnet Gravity

We consider a bi-connection model in the presence of four-dimensional Gauss-Bonnet term adding to the Einstein-Hilbert action. This generalization solves the dynamics issue which exists in pure Einstein-Hilbert formalism of bi-connection model. As an example we study the Weyl inspired bi-connection model and show there is a self-accelerating solution in this model. To compare it with previous results we try to find appropriate generalization of the Weyl geometrical bi-connection model to reach at de Rham-Gabadadze-Tolley massive gravity. In this formalism mixing terms between the potential and kinetic terms appear automatically.