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

TL;DR

This paper develops a novel mathematical framework to map and embed metrics representing ordinary matter, dark matter, and dark energy into a flat manifold, using advanced formalisms to unify these fundamental components of the universe.

Contribution

It introduces new formalisms for mapping and embedding different metrics in a flat manifold, extending previous approaches to include dark matter and dark energy.

Findings

Successfully maps metrics of different matter types

Embeds these metrics into a flat manifold

Provides a mathematical foundation for unifying matter components

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.