Gravitational Foundations and Exact Solutions in $n$--Dimensional Fractional Cosmology

TL;DR

This paper develops a fractional scalar field cosmological model in n dimensions using a time-dependent kernel weighted action, analyzing its gravitational features, exact solutions, and potential for bounce scenarios, with comparisons to standard models and data.

Contribution

It introduces a novel fractional cosmological model based on a specific fractional action, providing exact solutions and exploring its unique gravitational and dynamical properties.

Findings

Exact analytical solutions obtained for the fractional model.

Distinct gravitational features compared to standard cosmology.

Potential conditions for bounce solutions identified.

Abstract

Three theoretically plausible techniques to developing a fractional scalar field cosmological model are pointed in this paper; the time-dependent kernel weighted action being then selected. Upon this choice, we proceed to establish a fractional cosmological model in $n$ dimensions considering the FLRW metric and a generalized version of the S\'{a}ez-Ballester (SB) theory. Our study focuses on the following purposes. Firstly, to investigate the fundamental gravitational structural features of the model, we analyze the dynamical behavior of the field equations, the fulfillment of the Bianchi identities, the associated conservation laws, and the application of the second Noether theorem at the background and first-order perturbation levels. Moreover, the model's distinguishing characteristics and theoretical differences from the corresponding standard scenarios are also investigated. Secondly, we aim to obtain exact analytical solutions and analyze the time evolution of key cosmological quantities, considering the integration constants influence, and the number of spacetime dimensions, and the fractional parameter effects. Furthermore, the model's predictions are compared with those of the corresponding standard models and observational data. Lastly, we propose new ideas to further generalize our model, with a focus on constructing an effective potential and investigating the conditions under which bounce solutions may emerge.