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Gravity from self-interaction in a curved background

The full Einstein action is derived, by consistent self-coupling requirements, from the linear graviton action in an a priori arbitrary background geometry: flat space no longer plays a preferred initial role. This generalisation also permits construction of the cosmological term. An analogous procedure yields the Yang-Mills action starting from a Maxwell multiplet in a background gauge field. The relevant gauge invariances are shown to be under transformations in which the background is inert.