Emergent $Λ$CDM cosmology from a fractional extension of Newtonian gravity

Abstract: We propose a minimal single-parameter extension of Newtonian gravity obtained by introducing a time-dependent fractional kernel characterized by a deformation parameter $α$. This modification induces an effective fractional sector in the dynamics. Despite the appearance of a friction-like term in the equations of motion, we demonstrate the existence of a conserved quantity that contains a memory-like fractional kinetic contribution. By consistently generalizing the standard potential to an effective potential that depends on $α$, the resulting cosmological equations exhibit background dynamics that are dynamically equivalent to relativistic cosmology. Remarkably, with a single unified potential and without introducing a cosmological constant by hand, the radiation-dominated era, the matter-dominated era, and the present accelerated phase are simultaneously and self-consistently reproduced. The structural presence of $α$ in all physical observables allows theoretical and observational constraints to be imposed, indicating that compatibility with the data requires $|α- 1| \ll 1$. In the limit $α\to 1$, the theory smoothly reduces to standard Newtonian gravity. These results show that an emergent $Λ$CDM-like cosmological dynamics can arise from a single-parameter fractional deformation of Newtonian gravity.