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We obtain the effective field equations in a brane-world scenario within theframework of a DGP model where the action on the brane is an arbitrary functionof the Ricci scalar, ${\cal L}(R)$, and the bulk action includes a scalar fieldin the matter Lagrangian. We obtain the Friedmann equations and accelerationconditions in the presence of the bulk scalar field for the $R^n$ term infour-dimensional gravity.

Bulk scalar field in brane-worlds with induced gravity inspired by the ${\cal L}(R)$ term