Weyl fluid dark matter model tested on the galactic scale by weak
  gravitational lensing
  The higher dimensional Weyl curvature induces on the brane a new source of
gravity. This Weyl fluid of geometrical origin (reducing in the spherically
symmetric, static configuration to a dark radiation and dark pressure) modifies
space-time geometry around galaxies and has been shown to explain the flatness
of galactic rotation curves. Independent observations for discerning between
the Weyl fluid and other dark matter models are necessary. Gravitational
lensing could provide such a test. Therefore we study null geodesics and weak
gravitational lensing in the dark radiation dominated region of galaxies in a
class of spherically symmetric brane-world metrics. We find that the lensing
profile in the brane-world scenario is distinguishable from dark matter
lensing, despite both the brane-world scenario and dark matter models fitting
the rotation curve data. In particular, in the asymptotic regions light
deflection is 18% enhanced as compared to dark matter halo predictions. For a
linear equation of state of the Weyl fluid we further find a critical radius,
below which brane-world effects reduce, while above it they amplify light
deflection. This is in contrast to any dark matter model, the addition of which
always increases the deflection angle.
