Gravitational potential and galaxy rotation curves in multi-fractional spacetimes
Abstract Multi-fractional theories with integer-order derivatives are models of gravitational and matter fields living in spacetimes with variable Hausdorff and spectral dimension, originally proposed as descriptions of geometries arising in quantum gravity. We derive the Poisson equation and the Ne...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP08(2022)024 |
| _version_ | 1818504877217677312 |
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| author | Gianluca Calcagni Gabriele U. Varieschi |
| author_facet | Gianluca Calcagni Gabriele U. Varieschi |
| author_sort | Gianluca Calcagni |
| collection | DOAJ |
| description | Abstract Multi-fractional theories with integer-order derivatives are models of gravitational and matter fields living in spacetimes with variable Hausdorff and spectral dimension, originally proposed as descriptions of geometries arising in quantum gravity. We derive the Poisson equation and the Newtonian potential of these theories starting from their covariant modified Einstein’s equations. In particular, in the case of the theory T v with weighted derivatives with small fractional corrections, we find a gravitational potential that grows logarithmically at large radii when the fractional exponent takes the special value α = 4/3. This behaviour is associated with a restoration law for the Hausdorff dimension of spacetime independently found in the dark-energy sector of the same theory. As an application, we check whether this potential can serve as an alternative to dark matter for the galaxies NGC7814, NGC6503 and NGC3741 in the SPARC catalogue. We show that their rotation curves at medium-to-large radii can indeed be explained by purely geometric effects, although the Tully-Fisher relation is not reproduced well. We discuss how to fix the small-radius behaviour by lifting some approximations and how to test the model with other observables and an enlarged galaxy sample. |
| first_indexed | 2024-12-10T21:43:10Z |
| format | Article |
| id | doaj.art-db2d520689624ba0b48e419c520b1718 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-10T21:43:10Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-db2d520689624ba0b48e419c520b17182022-12-22T01:32:27ZengSpringerOpenJournal of High Energy Physics1029-84792022-08-012022817010.1007/JHEP08(2022)024Gravitational potential and galaxy rotation curves in multi-fractional spacetimesGianluca Calcagni0Gabriele U. Varieschi1Instituto de Estructura de la Materia, CSICDepartment of Physics, Loyola Marymount UniversityAbstract Multi-fractional theories with integer-order derivatives are models of gravitational and matter fields living in spacetimes with variable Hausdorff and spectral dimension, originally proposed as descriptions of geometries arising in quantum gravity. We derive the Poisson equation and the Newtonian potential of these theories starting from their covariant modified Einstein’s equations. In particular, in the case of the theory T v with weighted derivatives with small fractional corrections, we find a gravitational potential that grows logarithmically at large radii when the fractional exponent takes the special value α = 4/3. This behaviour is associated with a restoration law for the Hausdorff dimension of spacetime independently found in the dark-energy sector of the same theory. As an application, we check whether this potential can serve as an alternative to dark matter for the galaxies NGC7814, NGC6503 and NGC3741 in the SPARC catalogue. We show that their rotation curves at medium-to-large radii can indeed be explained by purely geometric effects, although the Tully-Fisher relation is not reproduced well. We discuss how to fix the small-radius behaviour by lifting some approximations and how to test the model with other observables and an enlarged galaxy sample.https://doi.org/10.1007/JHEP08(2022)024Classical Theories of GravityModels for Dark MatterModels of Quantum Gravity |
| spellingShingle | Gianluca Calcagni Gabriele U. Varieschi Gravitational potential and galaxy rotation curves in multi-fractional spacetimes Journal of High Energy Physics Classical Theories of Gravity Models for Dark Matter Models of Quantum Gravity |
| title | Gravitational potential and galaxy rotation curves in multi-fractional spacetimes |
| title_full | Gravitational potential and galaxy rotation curves in multi-fractional spacetimes |
| title_fullStr | Gravitational potential and galaxy rotation curves in multi-fractional spacetimes |
| title_full_unstemmed | Gravitational potential and galaxy rotation curves in multi-fractional spacetimes |
| title_short | Gravitational potential and galaxy rotation curves in multi-fractional spacetimes |
| title_sort | gravitational potential and galaxy rotation curves in multi fractional spacetimes |
| topic | Classical Theories of Gravity Models for Dark Matter Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP08(2022)024 |
| work_keys_str_mv | AT gianlucacalcagni gravitationalpotentialandgalaxyrotationcurvesinmultifractionalspacetimes AT gabrieleuvarieschi gravitationalpotentialandgalaxyrotationcurvesinmultifractionalspacetimes |