Mapping and Embedding of Two Metrics Associated with Dark Matter, Dark Energy, and Ordinary Matter

Abstract

In this paper we build a mapping between two different metrics and embed them in a flat manifold. One of the metrics represents the ordinary matter, and the other describes the dark matter, the dark energy, and the particle-antiparticle asymmetry. The latter was obtained in a recent paper. For the mapping and embedding, we use two new formalisms developed and presented in two previous papers, Mapping Among Manifolds and, Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate Transformations, which was a generalization of the Cartan's approach of Riemannian normal coordinates.