Emergent $\Lambda$CDM cosmology from a measure-induced deformation of the Newtonian action

Abstract

We propose a minimal extension of the Newtonian action by introducing a time-dependent fractional kernel characterized by a single deformation parameter $\alpha$. This kernel admits a natural interpretation as a nontrivial 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 effective $\alpha$-dependent 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 $\alpha =1$, 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 $\alpha$ in all physical observables allows theoretical and observational constraints to be imposed, indicating compatibility with observational data in the regime where $\alpha$ is close to unity. Within this framework, an effective cosmological constant naturally arises, controlled by the small deviation of $\alpha$ from the Newtonian limit. These results show that the proposed fractional framework can effectively reproduce the main background dynamical features of $\Lambda$CDM cosmology through a simple measure-induced deformation of the Newtonian action.

30 pages, no figures

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