A general guide to finding the ground state of a physical system is that it has a high degree of symmetry. For system where energy can be defined, the positive energy theorem tells us that the ground state for general relativity must be supersymmetric. Unfortunately, the real universe does not look like this. Conformal supersymmetry is a simple extension of these ideas. We show how to discover spacetime that have unbroken conformal supersymmetry, and relate this to solutions of the twistor equation. Finally we show that FRW spacetimes are conformally supersymmetric.