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arXiv · 2603.02124

On the Physical Nature of the Scalar Mode Mass in the Jordan frame of a Metric $f(R)$ gravity

Giovanni Montani·Andrea Valletta
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Abstract

We analyze the Taylor expansion of metric $f(R)$ gravity in the Jordan frame around the General Relativity limit. By relating the scalar--tensor representation to the original $f(R)$ formulation, we derive constraints on the expansion parameters from the observed value of the present-day $\Lambda$CDM deceleration parameter and from cosmological bounds on the variation of Newton's constant. We show that these requirements imply that the scalar degree of freedom must have a mass exceeding the Hubble scale by several orders of magnitude. This result challenges the common assumption that the scalar mode can drive cosmological dynamics with a mass of order $H_0$. We provide a dynamical interpretation of this hierarchy by emphasizing that a proper definition of the scalar mass, in a field-theoretical sense, requires an adiabatic separation between background evolution and perturbations, which naturally leads to a super-Hubble mass scale.

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Giovanni Montani, Andrea Valletta. 2026-03-02. On the Physical Nature of the Scalar Mode Mass in the Jordan frame of a Metric $f(R)$ gravity. https://doi.org/10.3390/sym18050714

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