Reconstruction Between Generalized Hybrid Metric--Palatini Gravity and $Φ(R,ϕ,X)$ Theories
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917464696160256 |
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| author | Ramírez, Jonathan |
| author_facet | Ramírez, Jonathan |
| contents | We develop a local reconstruction framework between $Φ(R,ϕ,X)$ theories with linear dependence on $X$ and generalized hybrid metric--Palatini gravity. The construction is formulated in vacuum in the Einstein frame, where both formulations can be written as two-scalar theories with the same field-space geometry. The framework provides a practical method for finding $Φ(R,ϕ,X)$ and $f(R,\mathcal R)$ functions that describe the same regular Einstein-frame two-scalar sector. Starting from a given $Φ(R,ϕ,X)$ model, we derive the equation that determines the compatible hybrid functions $f(R,\mathcal R)$ and show that it has a Clairaut-type structure. We also show that the inverse reconstruction is not unique: a regular hybrid Einstein-frame potential determines a family of compatible $Φ(R,ϕ,X)$ theories, parametrized by the kinetic coupling. Explicit examples illustrate the reconstruction procedure, its domain of validity, and the translation of model parameters between the $Φ(R,ϕ,X)$ and $f(R,\mathcal R)$ formulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05060 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reconstruction Between Generalized Hybrid Metric--Palatini Gravity and $Φ(R,ϕ,X)$ Theories Ramírez, Jonathan General Relativity and Quantum Cosmology We develop a local reconstruction framework between $Φ(R,ϕ,X)$ theories with linear dependence on $X$ and generalized hybrid metric--Palatini gravity. The construction is formulated in vacuum in the Einstein frame, where both formulations can be written as two-scalar theories with the same field-space geometry. The framework provides a practical method for finding $Φ(R,ϕ,X)$ and $f(R,\mathcal R)$ functions that describe the same regular Einstein-frame two-scalar sector. Starting from a given $Φ(R,ϕ,X)$ model, we derive the equation that determines the compatible hybrid functions $f(R,\mathcal R)$ and show that it has a Clairaut-type structure. We also show that the inverse reconstruction is not unique: a regular hybrid Einstein-frame potential determines a family of compatible $Φ(R,ϕ,X)$ theories, parametrized by the kinetic coupling. Explicit examples illustrate the reconstruction procedure, its domain of validity, and the translation of model parameters between the $Φ(R,ϕ,X)$ and $f(R,\mathcal R)$ formulations. |
| title | Reconstruction Between Generalized Hybrid Metric--Palatini Gravity and $Φ(R,ϕ,X)$ Theories |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.05060 |