On the Physical Nature of the Scalar Mode Mass in the Jordan frame of a Metric $f(R)$ gravity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915957340897280 |
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| author | Montani, Giovanni Valletta, Andrea |
| author_facet | Montani, Giovanni Valletta, Andrea |
| contents | 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 $Λ$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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_02124 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Physical Nature of the Scalar Mode Mass in the Jordan frame of a Metric $f(R)$ gravity Montani, Giovanni Valletta, Andrea General Relativity and Quantum Cosmology 83C25, 83F05, 83D05 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 $Λ$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. |
| title | On the Physical Nature of the Scalar Mode Mass in the Jordan frame of a Metric $f(R)$ gravity |
| topic | General Relativity and Quantum Cosmology 83C25, 83F05, 83D05 |
| url | https://arxiv.org/abs/2603.02124 |