  We derive the low energy effective theory on a brane in six-dimensional
chiral supergravity. The conical 3-brane singularities are resolved by
introducing cylindrical codimension one 4-branes whose interiors are capped by
a regular spacetime. The effective theory is described by the Brans-Dicke (BD)
theory with the BD parameter given by $\omega_{\rm BD}=1/2$. The BD field is
originated from a modulus which is associated with the scaling symmetry of the
system. If the dilaton potentials on the branes preserve the scaling symmetry,
the scalar field has an exponential potential in the Einstein frame. We show
that the time dependent solutions driven by the modulus in the four-dimensional
effective theory can be lifted up to the six-dimensional exact solutions found
in the literature. Based on the effective theory, we discuss a possible way to
stabilize the modulus to recover standard cosmology and also study the
implication for the cosmological constant problem.
