  In this paper a quantum N = 4 super Yang-Mills theory perturbed by
dilaton-coupled scalars, is considered. The induced effective action for such a
theory is calculated on a dilaton-gravitational background using the conformal
anomaly found via AdS/CFT correspondence. Considering such an effective action
(using the large N method) as a quantum correction to the classical gravity
action with cosmological constant we study the effect from dilaton to the scale
factor (which corresponds to the inflationary universe without dilaton). It is
shown that, depending on the initial conditions for the dilaton, the dilaton
may slow down, or accelerate, the inflation process. At late times, the dilaton
is decaying exponentially. At the end of this work, we consider the question
how the perturbation of the solution for the scale factor affects the stability
of the solution for the equations of motion and therefore the stability of the
Inflationary Universe, which could be eternal.
