A minimal fractional deformation of Newtonian gravity

TL;DR

This paper introduces a minimal fractional deformation of Newtonian gravity characterized by a parameter alpha, which can account for cosmic evolution, large-scale structure, and key Solar-System tests within a unified framework, potentially addressing fundamental cosmological problems.

Contribution

It demonstrates that a single fractional Newtonian model can describe cosmic history, structure growth, and Solar-System gravitational tests, unifying these phenomena under one parameterized framework.

Findings

The model reproduces the full cosmic evolution sequence.

It accounts for Solar-System tests like Mercury's perihelion precession.

The framework offers new perspectives on cosmological problems.

Abstract

We consider a minimal fractional deformation of Newtonian gravity characterized by a single parameter $\alpha$. In the limit $\alpha \to 1$, the theory reduces to standard Newtonian gravity. Previous works showed that the $\Lambda$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 $|\alpha-1|\ll1$, 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 $\alpha$. 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.