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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.03113 |
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Table of Contents:
- We propose a minimal extension of the Newtonian action by introducing a time-dependent fractional kernel characterized by a single deformation parameter $α$. This kernel admits a natural interpretation as a nontrivial temporal integration measure defined by a time-dependent kernel, placing the formulation within measure-based approaches to anomalous or fractal dynamics. Despite the appearance of a friction-like term in the equations of motion, a conserved quantity is still obtained, containing a memory-like fractional kinetic energy contribution. Moreover, by generalizing the standard Newtonian potential to an $α$-dependent effective potential induced by the underlying measure, the resulting cosmological equations exhibit an effective correspondence with relativistic FLRW cosmology at the level of background dynamics. In the limit $α=1$, the framework reduces to standard Newtonian cosmology. We show that, with a single unified potential, the matter-dominated, radiation-dominated, and present accelerated phases are obtained self-consistently, while the latter two epochs cannot be described within standard Newtonian cosmology. The structural presence of $α$ in all physical observables allows theoretical and observational constraints to be imposed, indicating that compatibility with observational data requires $|α- 1|\ll1$. Within this framework, an effective cosmological constant emerges, controlled by the small deviation of $α$ from the Newtonian limit. These results demonstrate that $Λ$CDM cosmological dynamics emerge from a simple measure-induced deformation of the Newtonian action.