How much in the Universe can be explained by geometry?

TL;DR

This paper explores how geometric principles in higher-dimensional spacetime can explain key cosmological phenomena, such as galaxy rotation curves and supernova observations, without invoking dark matter or dark energy.

Contribution

It introduces a geometric framework using monogenic functions in 5D spacetime to derive cosmological effects traditionally explained by dark matter and dark energy.

Findings

Derives the Hubble relation as a geometric effect.

Explains galaxy rotation curves without dark matter.

Accounts for supernovae observations without a cosmological constant.

Abstract

The paper uses geometrical arguments to derive equations with relevance for cosmology; 5-dimensional spacetime is assumed because it has been shown in other works to provide a setting for significant unification of different areas of physics. Monogenic functions, which zero the vector derivative are shown to effectively model electrodynamics and relativistic dynamics if one allows for space curvature. Applying monogenic functions to flat space, the Hubble relation can be derived straightforwardly as a purely geometrical effect. Consideration of space curvature induced by mass density allows the derivation of flat rotation curves for galaxies without appealing for dark matter. Similarly, a small overall mass density in the Universe is shown to provide a possible explanation for recent supernovae observations, without the need for a cosmological constant.