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

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.

arXiv comment13 pages, 3 figures, 3 tables. Accepted for publication in the Journal Symmetry

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• Cosmology under the fractional calculus approach
• Fractional-order derivatives in cosmological models of accelerated expansion
• Estimated Age of the Universe in Fractional Cosmology
• Emergence of fractal cosmic space from fractional quantum gravity
• Conformal and Non-Minimal Couplings in Fractional Cosmology
• Fractional Einstein-Gauss-Bonnet scalar field cosmology
• A vacuum solution of modified Einstein equations based on fractional calculus
• Is MOND necessarily nonlinear?
• Multidimensional representation of semantic relations between physical theories, fundamental constants and units of measurement with formal concept analysis
• Cosmology of fractional gravity
• Stability Analysis Of Fractional Relativistic Polytropes