Extending Friedmann equations using fractional derivatives using a Last Step Modification technique: the case of a matter dominated accelerated expanding Universe

TL;DR

This paper introduces a fractional calculus extension to Friedmann equations, using a Last Step Modification technique, to model the accelerated expansion of a matter-dominated universe without dark energy or dark matter.

Contribution

It develops a novel fractional derivative approach in cosmology, fitting observational data and explaining acceleration without dark energy or dark matter.

Findings

Fractional derivatives can model universe acceleration.

The model fits SN Ia data well.

Dark energy and dark matter may be unnecessary.

Abstract

We present a toy model for extending the Friedmann equations of relativistic cosmology using fractional derivatives. We do this by replacing the integer derivatives, in a few well-known cosmological results with fractional derivatives leaving their order as a free parameter. All this with the intention to explain the current observed acceleration of the Universe. We apply the Last Step Modification technique of fractional calculus to construct some useful fractional equations of cosmology. The fits of the unknown fractional derivative order and the fractional cosmographic parameters to SN Ia data shows that this simple construction can explain the current accelerated expansion of the Universe without the use of a dark energy component with a MOND-like behaviour using Milgrom's acceleration constant which sheds light into to the non-necessity of a dark matter component as well.