Revisiting Fractional Cosmology

TL;DR

This paper explores fractional calculus in cosmology, analyzing modified Friedmann equations and phase space dynamics to understand how fractional derivatives influence cosmological evolution and late-time acceleration.

Contribution

It extends previous work by analyzing scalar field cosmology with fractional derivatives, providing new insights into the physical interpretation of solutions.

Findings

Fractional order affects cosmological phase space structure.

Late-time power-law acceleration solutions are possible.

Fractional calculus can significantly influence cosmological models.

Abstract

Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting theory is compared against observational data. In this context, dynamical systems can be used along with an analysis the phase spaces for different values of the fractional order of the derivative and their different matter contents. The equilibrium points are classified, providing a range for the order of the fractional derivative in order to investigate whether the cosmological history can be reconstructed and a late-time accelerating power-law solution obtained for the scale factor. In this paper, we discuss the physical interpretation of the corresponding cosmological solutions with particular emphasis on the influence of the fractional order of the derivative in a theory of gravity that includes a scalar field minimally coupled to gravity. The presented results improve and extend those obtained previously, further demonstrating that fractional calculus can play a relevant role in cosmology.