General Coordinate Transformations as the Origins of Dark Energy

TL;DR

This paper explores how the algebra of coordinate transformations can give rise to a scalar field, the diffeomorphism scalar field, which may explain phenomena like dark energy, inflation, and dark matter in cosmology.

Contribution

It introduces the concept of the diffeomorphism scalar field derived from coordinate transformation algebras and explores its potential cosmological roles.

Findings

The diffeomorphism scalar field can act as dark energy or inflaton.

It can serve as a source of dark matter.

It may contribute to the cosmological constant Lambda.

Abstract

In this note we demonstrate that the algebra associated with coordinate transformations might contain the origins of a scalar field that can behave as an inflaton and/or a source for dark energy. We will call this particular scalar field the diffeomorphism scalar field. In one dimension, the algebra of coordinate transformations is the Virasoro algebra while the algebra of gauge transformations is the Kac-Moody algebra. An interesting representation of these algebras corresponds to certain field theories that have meaning in any dimension. In particular the so called Kac-Moody sector corresponds to Yang-Mills theories and the Virasoro sector corresponds to the diffeomorphism field theory that contains the scalar field and a rank-two symmetric, traceless tensor. We will focus on the contributions of the diffeomorphism scalar field to cosmology. We show that this scalar field can, qualitatively, act as a phantom dark energy, an inflaton, a dark matter source, and the cosmological constant Lambda.