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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.22937 |
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| _version_ | 1866915763620675584 |
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| author | Gervani, Lorenzo Diaferio, Antonaldo Pace, Francesco Sanna, Andrea Pierfrancesco |
| author_facet | Gervani, Lorenzo Diaferio, Antonaldo Pace, Francesco Sanna, Andrea Pierfrancesco |
| contents | We investigate the formation of the large-scale cosmic structure in a scalar-tensor theory of gravity belonging to the class of the Brans--Dicke theories. The universe contains baryonic matter alone and neither dark matter nor dark energy. The two arbitrary functions of the scalar field characterizing the kinetic term and the self-interaction potential are set to $W(φ)=-1$ and $V(φ) = -Ξφ$, respectively, with $Ξ$ a positive constant. In the weak-field limit, the theory reduces to Refracted Gravity, a non-relativistic theory whose modified Poisson equation contains the scalar field $φ$ that provides the gravitational boost required to describe the dynamics of galaxies and galaxy clusters without dark matter. In a flat, matter-dominated, homogeneous and isotropic universe the same scalar field $φ$ drives the accelerated expansion of the universe and describes the observed redshift evolution of the Hubble-Lemaître parameter $H(z)$. However, in the equation of the growth factor of the linear perturbation theory, the form of $V(φ)$ makes the coefficient of the source of the gravitational field proportional to $H^{-1}(z)$; therefore the gravitational field is strongly suppressed at early times and structure formation is delayed to redshift $z< 1$, in disagreement with the observation of formed galaxies at much larger redshifts. In addition, the form of $W(φ)$ and a linear $V(φ)$ imply that $φ$ generates twice the gravitational boost on massive particles than on photons, with possible observable consequences on the gravitational lensing phenomenon. It remains to be investigated whether different choices of $W(φ)$ and $V(φ)$, that can still make the theory reduce to Refracted Gravity in the weak-field limit, might alleviate these problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_22937 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear perturbation theory and structure formation in a Brans-Dicke theory of gravity without dark matter Gervani, Lorenzo Diaferio, Antonaldo Pace, Francesco Sanna, Andrea Pierfrancesco Cosmology and Nongalactic Astrophysics We investigate the formation of the large-scale cosmic structure in a scalar-tensor theory of gravity belonging to the class of the Brans--Dicke theories. The universe contains baryonic matter alone and neither dark matter nor dark energy. The two arbitrary functions of the scalar field characterizing the kinetic term and the self-interaction potential are set to $W(φ)=-1$ and $V(φ) = -Ξφ$, respectively, with $Ξ$ a positive constant. In the weak-field limit, the theory reduces to Refracted Gravity, a non-relativistic theory whose modified Poisson equation contains the scalar field $φ$ that provides the gravitational boost required to describe the dynamics of galaxies and galaxy clusters without dark matter. In a flat, matter-dominated, homogeneous and isotropic universe the same scalar field $φ$ drives the accelerated expansion of the universe and describes the observed redshift evolution of the Hubble-Lemaître parameter $H(z)$. However, in the equation of the growth factor of the linear perturbation theory, the form of $V(φ)$ makes the coefficient of the source of the gravitational field proportional to $H^{-1}(z)$; therefore the gravitational field is strongly suppressed at early times and structure formation is delayed to redshift $z< 1$, in disagreement with the observation of formed galaxies at much larger redshifts. In addition, the form of $W(φ)$ and a linear $V(φ)$ imply that $φ$ generates twice the gravitational boost on massive particles than on photons, with possible observable consequences on the gravitational lensing phenomenon. It remains to be investigated whether different choices of $W(φ)$ and $V(φ)$, that can still make the theory reduce to Refracted Gravity in the weak-field limit, might alleviate these problems. |
| title | Linear perturbation theory and structure formation in a Brans-Dicke theory of gravity without dark matter |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2601.22937 |