On the Dark‐Energy Enigma

A model is presented that provides 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–Lemaître universe are presented.