We study the dynamics of a flat Friedmann-Robertson-Walker universe filled with a self-interacting scalar field nonminimally coupled to the gravitational field. Dynamical equations for the system can be derived from a pointlike Lagrangian. For this system an additional Nother symmetry exists provided that the coupling constant 6 is equal to 0 or i. When l= $ the scalar potential has to be constant. In this case we obtain an exact solution. We also analyze the behavior of the scalar field when S f 0, i .Most of the considered solutions are unphysical but there exists a very interesting case in which the effective cosmological constant is rapidly changing, which might lead to inflation.
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