Four Dimensional Conformal Gravity, Confinement, and Galactic Rotation Curves

TL;DR

This paper reviews conformal gravity as an alternative to Einstein's theory, exploring its potential in particle physics and explaining galactic rotation curves without dark matter.

Contribution

It presents a comprehensive analysis of conformal gravity's theoretical foundations and its application to galactic dynamics, proposing it as a viable alternative to dark matter explanations.

Findings

Conformal gravity can produce a confining potential explaining galactic rotation curves.

The theory retains key tested features of Einstein gravity while offering new insights.

It suggests conformal gravity as a candidate for a fundamental microscopic theory of gravity.

Abstract

We review the current status and prospects for the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. We examine how it is possible in principle to replace the Einstein theory at all while retaining its tested features, and we appeal to the wisdom gleaned from particle physics to suggest a fully covariant, conformal invariant alternative. We explore the theory as a microscopic fundamental theory of elementary particles, to thus give curvature a more prominent role in elementary particle dynamics, and in particular in the generation both of elementary particle masses and the extended bag-like models which are thought to describe them. We discuss the degree to which conformal gravity can compete with string theory as a consistent candidate microscopic theory of gravity. Additionally, we explore the theory as a macroscopic theory of gravity where the exact, non-perturbative, classical potential is found to be of the confining $V(r)=-\beta /r+\gamma r/2$ form, a form which enables us to provide an explanation for the general systematics of galactic rotational velocity curves without the need to assume the existence of copious amounts of dark matter; with this explanation of the curves apparently not being in conflict with the current round of microlensing observations.