Quantization of the Bianchi type-IX model in supergravity with a cosmological constant

Diagonal Bianchi type-IX models are studied in the quantum theory of $N=1\mathrm{}$ supergravity with a cosmological constant. It is shown, by imposing the supersymmetry and Lorentz quantum constraints, that there are no physical quantum states in this model. The $k=+1\mathrm{}$ Friedmann model in supergravity with a cosmological constant does admit quantum states. However, the Bianchi type-IX model provides a better guide to the behavior of a generic state, since more gravitino modes are available to be excited. These results indicate that there may be no physical quantum states in the full theory of $N=1\mathrm{}$ supergravity with a nonzero cosmological constant.