Emergent Inflation in Fractional Cosmology
- 1Departamento de Física, Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200-001 Covilhã, Portugal
Abstract
We investigate the dynamics of the early universe within an emergent fractional cosmological framework generated by a measure-deformed Newtonian action, without introducing additional propagating degrees of freedom. Considering asymptotic and dynamical requirements, we construct a minimal fractional potential that, together with the time-dependent fractional kernel, generates a regular pre-inflationary stage, quasi-de Sitter inflation, a dynamically controlled exit, and a subsequent finite duration radiation-like phase. The exact solution of the reduced early-time equation is obtained in two equivalent representations, and regularity selects a unique physical branch with finite principal curvature invariants at the initial boundary. Remarkably, the same exact trajectory evolves asymptotically toward the quasi-de Sitter regime, while an exact nonlinear analysis of homogeneous Hubble deviations establishes its asymptotic attractor character within the admissible expanding sector. Inflation ends dynamically near the zero crossing of the effective fractional force, leading to controlled background-level consistency relations among the inflationary duration, the fractional parameter, the effective equation of state parameter, and the exit scale. For the physically relevant post-inflationary regime, the model admits the characteristic radiation-like expansion over a finite post-inflationary interval. These results show that a coherent sequence of regular pre-inflationary, inflationary, and post-inflationary background dynamics can emerge from a simple and unified fractional Newtonian framework without invoking an inflaton field.
Related
- Rank-one variance inflation in polynomial estimation of signal parameters with a sign-preserving fractional-power basis
- An Improved Minimization Method: Eliminating Shift and Variance Inflation While Maintaining Marginal Balance
- Norm inflation and loss of regularity in negative Sobolev spaces for KdV and KP
- Low Regularity Norm Inflation of Axisymmetric Hall Magnetohydrodynamics in Sobolev Space
- Discussion on "Principled type I error rate inflation in two-arm clinical trial designs with external control information borrowing" by Silvia Calderazzo, Manuel Wiesenfarth, Vivienn Weru, and Annette Kopp-Schneider
BibTeX
@article{rasouli2026emergent,
title = {{Emergent Inflation in Fractional Cosmology}},
author = {S. M. M. Rasouli},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10110757},
url = {https://www.mdpi.com/2504-3110/10/11/757},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Emergent Inflation in Fractional Cosmology
AU - S. M. M. Rasouli
PY - 2026
DA - 2026/10/29
JO - Fractal and Fractional
DO - 10.3390/fractalfract10110757
UR - https://www.mdpi.com/2504-3110/10/11/757
AB - We investigate the dynamics of the early universe within an emergent fractional cosmological framework generated by a measure-deformed Newtonian action, without introducing additional propagating degrees of freedom. Considering asymptotic and dynamical requirements, we construct a minimal fractional potential that, together with the time-dependent fractional kernel, generates a regular pre-inflationary stage, quasi-de Sitter inflation, a dynamically controlled exit, and a subsequent finite duration radiation-like phase. The exact solution of the reduced early-time equation is obtained in two equivalent representations, and regularity selects a unique physical branch with finite principal curvature invariants at the initial boundary. Remarkably, the same exact trajectory evolves asymptotically toward the quasi-de Sitter regime, while an exact nonlinear analysis of homogeneous Hubble deviations establishes its asymptotic attractor character within the admissible expanding sector. Inflation ends dynamically near the zero crossing of the effective fractional force, leading to controlled background-level consistency relations among the inflationary duration, the fractional parameter, the effective equation of state parameter, and the exit scale. For the physically relevant post-inflationary regime, the model admits the characteristic radiation-like expansion over a finite post-inflationary interval. These results show that a coherent sequence of regular pre-inflationary, inflationary, and post-inflationary background dynamics can emerge from a simple and unified fractional Newtonian framework without invoking an inflaton field.
SN - 2504-3110
ER -