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Essential nature of Newton’s constant in unimodular gravity

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Abstract

We point out that in unimodular gravity Newton’s constant is an essential coupling, i.e. it is independent of field redefinitions. We illustrate the consequences of this fact by a calculation in a standard simple approximation, showing that in this case the renormalization group flow of Newton’s constant is gauge and parametrization independent.

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Notes

  1. In order to do the functional variation, we can either remember that the linear perturbation must be traceless, and thus straightforwardly obtain the traceless equations (2.3), or we can include the unimodular constraint in the action by means of a Lagrange multiplier and then eliminate the latter from the equations of motion, obtaining of course the same result.

  2. Note that because \(h_\mu ^\mu =0\) we have only two possible ultralocal terms at order \(\epsilon ^2\) instead of the general four discussed in [28].

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  1. Laboratoire de Physique Théorique, CNRS UMR 8627, Bât. 210, Université Paris-Sud, 91405, Orsay Cedex, France

    Dario Benedetti

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Benedetti, D. Essential nature of Newton’s constant in unimodular gravity. Gen Relativ Gravit 48, 68 (2016). https://doi.org/10.1007/s10714-016-2060-3

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