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.
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James E. Lidsey (1995) studied this question.
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