  The low energy effective theory for the Randall-Sundrum two brane system is
investigated with an emphasis on the role of the non-linear radion in the brane
world. The equations of motion in the bulk is solved using a low energy
expansion method. This allows us, through the junction conditions, to deduce
the effective equations of motion for the gravity on the brane. It is shown
that the gravity on the brane world is described by a quasi-scalar-tensor
theory with a specific coupling function omega(Psi) = 3 Psi / 2(1-Psi) on the
positive tension brane and omega(Phi) = -3 Phi / 2(1+Phi) on the negative
tension brane, where Psi and Phi are non-linear realizations of the radion on
the positive and negative tension branes, respectively. In contrast to the
usual scalar-tensor gravity, the quasi-scalar-tensor gravity couples with two
kinds of matter, namely, the matters on both positive and negative tension
branes, with different effective gravitational coupling constants. In
particular, the radion disguised as the scalar fields Psi and Phi couples with
the sum of the traces of the energy momentum tensor on both branes. In the
course of the derivation, it has been revealed that the radion plays an
essential role to convert the non-local Einstein gravity with the generalized
dark radiation to the local quasi-scalar-tensor gravity. For completeness, we
also derive the effective action for our theory by substituting the bulk
solution into the original action. It is also shown that the
quasi-scalar-tensor gravity works as holograms at the low energy in the sense
that the bulk geometry can be reconstructed from the solution of the
quasi-scalar-tensor gravity.
