Fractional Scalar Field Cosmology

TL;DR

This paper explores fractional scalar field cosmology using fractional calculus to derive exact solutions within FLRW models, revealing new potentials and proposing an inflationary scenario in a fractional quantum framework.

Contribution

It introduces a novel fractional calculus approach to scalar field cosmology, deriving exact solutions and determining scalar potentials from fractional field equations.

Findings

Exact solutions for fractional scalar field models

Scalar potentials derived from fractional field equations

An inflationary scenario in fractional quantum cosmology

Abstract

Considering the Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) metric and the Einstein scalar field system as an underlying gravitational model to construct fractional cosmological models has interesting implications in both classical and quantum regimes. Regarding the former, we just review the most fundamental approach to establishing an extended cosmological model. We demonstrate that employing new methodologies allows us to obtain exact solutions. Despite the corresponding standard models, we cannot use any arbitrary scalar potentials; instead, it is determined from solving three independent fractional field equations. This article concludes with an overview of a fractional quantum/semi-classical model that provides an inflationary scenario.