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

TL;DR

This paper introduces a measure-induced deformation of Newtonian gravity with a parameter , leading to emergent CDM cosmology, including accelerated expansion, consistent with observations.

Contribution

It presents a novel measure-based extension of Newtonian gravity that reproduces key features of CDM cosmology with a single deformation parameter.

Findings

The framework recovers standard Newtonian cosmology at .

It self-consistently models matter, radiation, and accelerated phases.

An effective cosmological constant arises from the deformation parameter.

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 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 $\alpha$-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 $\alpha=1$, 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 that compatibility with observational data requires $|\alpha - 1|\ll1$. Within this framework, an effective cosmological constant emerges, controlled by the small deviation of $\alpha$ from the Newtonian limit. These results demonstrate that $\Lambda$CDM cosmological dynamics emerge from a simple measure-induced deformation of the Newtonian action.