On the Physical Nature of the Scalar Mode Mass in the Jordan Frame of Metric f(R) Gravity

We analyze the Taylor expansion of the metric f(R) gravity in the Jordan frame around the General Relativity limit, expanding in the small deviation (ϕ−ϕ0) with ϕ0=1. 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 ΛCDM (Λ Cold Dark Matter) 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 of the Hubble constant H0. 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.