Abstract
A version of the virial theorem is derived in a brane-world scenario in the framework of a warped DGP model where the action on the brane is an arbitrary function of the Ricci scalar, \(\mathcal{L}(R)\). The extra terms in the modified Einstein equations generate an equivalent mass term (geometrical mass), which give an effective contribution to the gravitational energy and offer viable explanation to account for the virial mass discrepancy in clusters of galaxies. We also obtain the radial velocity dispersion of galaxy clusters and show that it is compatible with the radial velocity dispersion profile of such clusters. Finally, we compare the result of the model with \(\mathcal{L}(R)\) gravity theories.
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