Scale Factor Duality and Hidden Supersymmetry in Scalar--Tensor Cosmology

It is shown that spatially flat, isotropic cosmologies derived from the Brans–Dicke gravity action exhibit a scale factor duality invariance. This classical duality is then associated with a hidden $N=2$ supersymmetry at the quantum level and the supersymmetric quantum constraints are solved exactly. These symmetries also apply to a dimensionally reduced version of vacuum Einstein gravity.