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The Hierarchy Problem in Particle Physics
It is natural to imagine that supersymmetry plays a role in explaining why the inflatan potential has the special properties. But it doesn't need to be, you can just do it without supersymmetry anyway. As far as I know, and again, not an expert on the most recent wrinkles here, this is completely unaffected by the fact that we have not seen supersymmetry at the large Hadron Collider. The hierarchy problem was purportedly going to be solved by discovering broken supersymmetry near the electroweak scale. And maybe we will, maybe we'll tomorrow, but we could have by now and we didn't.