Supersymmetric higher-derivative models in quantum cosmology

We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the bosons, and first order for the fermions. Upon quantization, the algebra of fermions leads to a multi-component state, which is annihilated by the Hamiltonian and supersymmetric constraint operators. We obtain asymptotic wave functions of the oscillatory type, whose classical limit corresponds to inflationary evolution, and exact exponential wave functions. We use the latter to derive probability distributions of the initial curvature that are compatible with those obtained using the non-supersymmetric model.