Can extra-dimensional effects replace dark matter?

In the braneworld scenario, the four-dimensional effective Einstein equation has extra terms which arise from the embedding of the 3-brane in the bulk. We show that in this modified theory of gravity, it is possible to model observations of galaxy rotation curves and the X-ray profiles of clusters of galaxies, without the need for dark matter. In this scenario, a traceless tensor field which arises from the projection of the bulk Weyl tensor on the brane, provides the extra gravitational acceleration which is usually explained through dark matter. We also predict that gravitational lensing observations can possibly discriminate between the proposed higher-dimensional effects and dark matter, the deflection angles predicted in the proposed scenario being around 75% to 80% of the usual predictions based on dark matter.