  We study the quantization of some cosmological models within the theory of
N=1 supergravity with a positive cosmological constant. We find, by imposing
the supersymmetry and Lorentz constraints, that there are no physical states in
the models we have considered. For the k=1 Friedmann-Robertson-Walker model,
where the fermionic degrees of freedom of the gravitino field are very
restricted, we have found two bosonic quantum physical states, namely the
wormhole and the Hartle-Hawking state.
  From the point of view of perturbation theory, it seems that the
gravitational and gravitino modes that are allowed to be excited in a
supersymmetric Bianchi-IX model contribute in such a way to forbid any physical
solutions of the quantum constraints. This suggests that in a complete
perturbation expansion we would have to conclude that the full theory of N=1
supergravity with a non-zero cosmological constant should have no physical
states.
