Quantization of the Bianchi type-IX model in supergravity.

Diagonal Bianchi type-IX models are studied in the quantum theory of N = 1 super-gravity 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 Friedmann model in supergravity with cosmological constant does admit quantum states. However, the Bianchi type-IX model provides a better guide to the behaviour 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 supergravity with a non-zero cosmological constant.