  We develop a formalism to calculate the effective action of the strongly
coupled conformal field theory (CFT) in curved spacetime. The effective action
of the CFT is obtained from AdS/CFT correspondence. The anti de-Sitter (AdS)
spacetime has various slicing which give various curved spacetime on its
boundary. We show the de Sitter spacetime and the Friedmann-Robertson-Walker
(FRW) universe can be embedded in the AdS spacetime and derive the scalar
two-point function of the conformal fields in those spacetime. In curved
spacetime, the two-point function depends on the vacuum state of the CFT. A
method to specify the vacuum state in AdS/CFT calculations is shown. Because
the classical action in AdS spacetime diverges near the boundary, we need the
counter terms to regulate the result. The simple derivation of the counter
terms using the Hamilton-Jacobi equation is also presented in the appendix.
