Conformal theory of central surface density for galactic dark halos

TL;DR

This paper proposes a conformal gravity theory that explains the near-universal central surface density of galactic dark halos without dark matter, using a nonclassical acceleration derived from Weyl symmetry.

Contribution

It introduces a conformal gravity framework with Weyl symmetry that predicts a universal central surface density for galactic halos, eliminating the need for dark matter.

Findings

Conformal gravity predicts a constant nonclassical acceleration in galactic halos.

Universal central surface density emerges naturally from the conformal model.

The model aligns with observational constraints on galactic acceleration profiles.

Abstract

Numerous dark matter studies of galactic halo gravitation depend on models with core radius $r_0$ and central density $\rho_0$. Central surface density product $\rho_0 r_0$ is found to be nearly a universal constant for a large range of galaxies. Standard variational field theory with Weyl conformal symmetry postulated for gravitation and the Higgs scalar field, without dark matter, implies nonclassical centripetal acceleration $\Delta a$, for $a=a_N+\Delta a$, where Newtonian acceleration $a_N$ is due to observable baryonic matter. Neglecting a halo cutoff at very large galactic radius, conformal $\Delta a$ is constant over the entire halo and $a=a_N+\Delta a$ is a universal function, consistent with a recent study of galaxies that constrains acceleration due to dark matter or to alternative theory. An equivalent dark matter source is a pure cusp distribution with cutoff parameter determined by a halo boundary radius. This is shown here to imply universal central surface density for any dark matter core model.