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We show that Renormalization Group extensions of the Einstein-Hilbert actionfor large scale physics are not, in general, a particular case of standardScalar-Tensor (ST) gravity. We present a new class of ST actions, in which thepotential is not necessarily fixed at the action level, and show that thisextended ST theory formally contains the Renormalization Group case. We alsopropose here a Renormalization Group scale setting identification that isexplicitly covariant and valid for arbitrary relativistic fluids.

Scalar-Tensor gravity with system-dependent potential and its relation with Renormalization Group extended General Relativity