Modular Quantum Cosmology

We study solutions of the Wheeler-DeWitt equation corresponding to an S-modular invariant N=1 supergravity model and a closed homogeneous and isotropic Friedmann-Robertson-Walker spacetime. The issues of inflation and of the cosmological constant problem are addressed with the help of the relevant wave functions. We find that topological type inflation is consistent from the quantum mechanical point of view and that a solution for the cosmological constant problem along the lines of the strong CP problem naturally arises.