  We derive a low-energy effective theory for gravity with anti-D branes, which
are essential to get de Sitter solutions in the type IIB string warped
compactification, by taking account of gravitational backreactions of anti-D
branes. In order to see the effects of the self-gravity of anti-D branes, a
simplified model is studied where a 5-dimensional anti-de Sitter ({\it AdS})
spacetime is realized by the bulk cosmological constant and the 5-form flux,
and anti-D branes are coupled to the 5-form field by Chern-Simon terms. The
{\it AdS} spacetime is truncated by introducing UV and IR cut-off branes like
the Randall-Sundrum model. We derive an effective theory for gravity on the UV
brane and reproduce the familiar result that the tensions of the anti-D branes
give potentials suppressed by the forth-power of the warp factor at the
location of the anti-D branes. However, in this simplified model, the potential
energy never inflates the UV brane, although the anti-D-branes are inflating.
The UV brane is dominated by dark radiation coming from the projection of the
5-dimensional Weyl tensor, unless the moduli fields for the anti-D branes are
stabilized. We comment on the possibility of avoiding this problem in a
realistic string theory compactification.
