Abstract
We discuss gravitational physics in the Jordan and Einstein frames of f(R) gravity coupled to the Standard Model. We elucidate the way in which the observed gravitational coupling arises in the Einstein frame for generic f(R). We point out that the effect of “running units” in the Einstein frame is related to the fact that the explicit and implicit quantum parameters of the Standard Model, such as the Higgs vacuum expectation value and the parameter ΛQCD, are modified by the conformal transformation of the metric and matter fields and become scalaron-dependent. Considering the scalaron of f(R) gravity describing dark matter, we show that the effect of running units in this case is extremely weak, making two frames practically equivalent.
Highlights
IntroductionAccording to our current understanding, this Lagrangian is to be regarded as an asymptotic local limit of the renormalisation-group flow
Working in the Einstein frame, we are going to estimate potential observable effects of f ( R) gravity in a late-time universe in which the oscillating scalaron plays the role of dark matter [6,11]
Its physical value in the Einstein frame is uniquely determined by the function f ( R), together with the matter action in the Jordan frame
Summary
According to our current understanding, this Lagrangian is to be regarded as an asymptotic local limit of the renormalisation-group flow The physics that this theory describes at finite energy scales is characterised by physical constants arising from the phenomenon known as dimensional transmutation. As regards the masses of bound states such as hadrons, they depend in a non-trivial way on the implicit dimensionful quantum parameters such as ΛQCD This opens up two possibilities of interpreting the theory in the Einstein frame: as a theory with running implicit parameters (which becomes the frame with running mass units), equivalent to the theory in the original Jordan frame, or as a theory with fixed implicit parameters.
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