A minimal fractional deformation of Newtonian gravity
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915868315746304 |
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| author | Rasouli, S. M. M. |
| author_facet | Rasouli, S. M. M. |
| contents | We consider a minimal fractional deformation of Newtonian gravity characterized by a single parameter $α$. In the limit $α\to 1$, the theory reduces to standard Newtonian gravity. Previous works showed that the $Λ$CDM cosmology consistently emerges from this framework. Using a single potential, the model reproduces the full sequence of cosmic evolution (from a nonsingular pre--inflationary phase and a stable inflationary attractor to the radiation- and matter-dominated eras and the present accelerated expansion) and accounts for the growth of large-scale structure for $|α-1|\ll1$, in agreement with current observations. Here we show that the same fractional Newtonian model also describes key weak--field tests, including the perihelion precession of Mercury and the gravitational deflection of light, using a unified potential with the same constraint on $α$. These results suggest that the minimal fractional Newtonian framework may provide a unified phenomenological description of gravitational dynamics from Solar-System scales to cosmology. Finally, this fractional cosmological framework may offer new perspectives on problems such as the cosmological constant, the hierarchy of cosmological scales, and the Hubble tension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16009 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A minimal fractional deformation of Newtonian gravity Rasouli, S. M. M. General Relativity and Quantum Cosmology We consider a minimal fractional deformation of Newtonian gravity characterized by a single parameter $α$. In the limit $α\to 1$, the theory reduces to standard Newtonian gravity. Previous works showed that the $Λ$CDM cosmology consistently emerges from this framework. Using a single potential, the model reproduces the full sequence of cosmic evolution (from a nonsingular pre--inflationary phase and a stable inflationary attractor to the radiation- and matter-dominated eras and the present accelerated expansion) and accounts for the growth of large-scale structure for $|α-1|\ll1$, in agreement with current observations. Here we show that the same fractional Newtonian model also describes key weak--field tests, including the perihelion precession of Mercury and the gravitational deflection of light, using a unified potential with the same constraint on $α$. These results suggest that the minimal fractional Newtonian framework may provide a unified phenomenological description of gravitational dynamics from Solar-System scales to cosmology. Finally, this fractional cosmological framework may offer new perspectives on problems such as the cosmological constant, the hierarchy of cosmological scales, and the Hubble tension. |
| title | A minimal fractional deformation of Newtonian gravity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.16009 |