Geometrization of light bending and its application to SdSw spacetime
  The mysterious dark energy remains one of the greatest puzzles of modern
science. Current detections for it are mostly indirect. The spacetime effects
of dark energy can be locally described by the SdSw metric. Understanding these
local effects exactly is an essential step towards the direct probe of dark
energy. From first principles, we prove that dark energy can exert a repulsive
dark force on astrophysical scales, different from the Newtonian attraction of
both visible and dark matter. One way of measuring local effects of dark energy
is through the gravitational deflection of light. We geometrize the bending of
light in any curved static spacetime. First of all, we define a generalized
deflection angle, referred to as the Gaussian deflection angle, in a
mathematically strict and conceptually clean way. Basing on the Gauss-Bonnet
theorem, we then prove that the Gaussian deflection angle is equivalent to the
surface integral of the Gaussian curvature over a chosen lensing patch. As an
application of the geometrization, we study the problem of whether dark energy
affects the bending of light and provide a strict solution to this problem in
the SdSw spacetime. According to this solution, we propose a method to overcome
the difficulty of measuring local dark energy effects. Exactly speaking, we
find that the lensing effect of dark energy can be enhanced by 14 orders of
magnitude when properly choosing the lensing patch in certain cases. It means
that we can probe the existence and nature of dark energy directly in our Solar
System. This points to an exciting direction to help unraveling the great
mystery of dark energy.
