Abstract
The concepts of fragility and rigidity in theories containing a minimally coupled, self-interacting scalar field are introduced and defined for an arbitrary space-time dimension,D, by using the field as the dynamical variable. It is proved that inflation is rigid and the case of an exponential self-interaction is studied. The fragility of higher-order, scalar-tensor and Kaluza-Klein gravity theories is investigated by using their conformal equivalence to general relativity plus a scalar field. Whilst most higher-order theories are rigid, the conditions for Kaluza-Klein theories to become fragile depend strongly onD.
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