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The higher dimensional Weyl curvature induces on the brane a new source ofgravity. This Weyl fluid of geometrical origin (reducing in the sphericallysymmetric, static configuration to a dark radiation and dark pressure) modifiesspace-time geometry around galaxies and has been shown to explain the flatnessof galactic rotation curves. Independent observations for discerning betweenthe Weyl fluid and other dark matter models are necessary. Gravitationallensing could provide such a test. Therefore we study null geodesics and weakgravitational lensing in the dark radiation dominated region of galaxies in aclass of spherically symmetric brane-world metrics. We find that the lensingprofile in the brane-world scenario is distinguishable from dark matterlensing, despite both the brane-world scenario and dark matter models fittingthe rotation curve data. In particular, in the asymptotic regions lightdeflection is 18% enhanced as compared to dark matter halo predictions. For alinear equation of state of the Weyl fluid we further find a critical radius,below which brane-world effects reduce, while above it they amplify lightdeflection. This is in contrast to any dark matter model, the addition of whichalways increases the deflection angle.

Weyl fluid dark matter model tested on the galactic scale by weak gravitational lensing