On the Dark-Energy Enigma

TL;DR

This paper introduces a novel theoretical model that explains dark matter and dark energy as emergent phenomena from a scalar field and a three-form in a modified gravity framework, with solutions for cosmological models.

Contribution

It proposes a new scalar and three-form based model that extends mimetic gravity to account for dark energy and dark matter phenomena.

Findings

Derived field equations for the model.

Presented solutions in Friedmann-Lemaître universe.

Discussed the relation to topological winding numbers.

Abstract

We present a model that offers an explanation for the presence of (Dark Matter and) Dark Energy in the universe. A key idea is to express the volume form of the Lorentzian metric on space-time in terms of a positive function of a new scalar field multiplying a certain four-form given by the wedge product of the differential of the mimetic scalar field and a certain closed three-form. An ansatz for this three-form related to one commonly used to determine the winding number of a map from a three-dimensional hypersurface to a three-sphere is discussed. An action functional depending on the space-time metric, the new scalar field, the mimetic scalar and the three-form is proposed, and the field equations are derived. Special solutions of these equations for a Friedmann-Lema\^itre universe are presented.