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Non-minimal tinges of unimodular gravity. (English) Zbl 1454.83038
Summary: Unimodular Gravity is normally assumed to be equivalent to General Relativity for all matters but the character of the Cosmological Constant. Here we discuss this equivalence in the presence of a non-minimally coupled scalar field. We show that when we consider gravitation to be dynamical in a QFT sense, quantum corrections can distinguish both theories if the non-minimal coupling is non-vanishing. In order to show this, we construct a path integral formulation of Unimodular Gravity, fixing the complicated gauge invariance of the theory and computing all one-loop divergences. We find a combination of the couplings in the Lagrangian to which we can assign a physical meaning. It tells whether quantum gravitational phenomena can be ignored or not at a given energy scale. Its renormalization group flow differs depending on if it is computed in General Relativity or Unimodular Gravity.
83C45 Quantization of the gravitational field
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
81T17 Renormalization group methods applied to problems in quantum field theory
FORM ; xPert; xTras
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