Emergent inflation in fractional cosmology

TL;DR

This paper explores a fractional cosmology model where inflation emerges naturally from a non-singular pre-inflationary state, driven by a fractional potential without external fields, aligning with observational constraints.

Contribution

It introduces a novel fractional cosmological framework that produces emergent inflation as a stable attractor, linking fractional parameters to observable inflationary features.

Findings

Inflation arises dynamically without external scalar fields.

The model provides a graceful exit from inflation.

A relation between e-folds and fractional parameter $oldsymbol{ extalpha}$ is established.

Abstract

In this paper, we investigate the evolution of the early universe within an emergent fractional cosmological framework. The underlying formulation is conceptually rooted in generalized measure constructions, closely related to fractal geometries and scale-dependent effective dimensions. By constructing a suitable fractional potential, we show that the cosmological evolution naturally originates from a non-singular pre-inflationary regime. Inflation arises dynamically without introducing an external scalar field and emerges as a stable attractor, exhibiting similarities with plateau-type inflationary scenarios. By analyzing the dynamical transition, we determine the end of inflation and establish a meaningful relation between the number of e-folds and the fractional parameter $\alpha$, ensuring consistency with observations and addressing the horizon problem. Moreover, the model admits a graceful exit from inflation, followed by an exact radiation-dominated solution with the standard time dependence and an $\alpha$-dependent normalization.