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Scale invariant (transverse) gravitational theories are introduced. They are invariant under pure metric rescalings (i.e. the matter fields are inert under those). This symmetry forbids the presence of a cosmological constant. Those theories are not invariant under the full set of diffeomorphisms, but only with respect to those locally characterized by the fact that their generator is transverse ∂_αξ^α=0.
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Álvarez et al. (2010) studied this question.
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