Conformal Gravity Rotation Curves with a Conformal Higgs Halo

TL;DR

This paper explores how a conformally coupled Higgs field modifies conformal gravity predictions for galaxy rotation curves, showing that the Higgs field's radial profile cancels the linear potential used to fit observations without dark matter.

Contribution

It introduces a specific Higgs field profile in conformal gravity, demonstrating its effect on galaxy rotation curves and providing equations for astrophysical tests.

Findings

Higgs field profile cancels the linear potential in CG

Particle rest masses vary with radius due to S(r)

Formulation of CG equations for spherical structures with Higgs halos

Abstract

We discuss the effect of a conformally coupled Higgs field on conformal gravity (CG) predictions for the rotation curves of galaxies. The Mannheim-Kazanas (MK) metric is a valid vacuum solution of CG's 4-th order Poisson equation only if the Higgs field has a particular radial profile, S(r)=S_0 a/(r+a), decreasing from S_0 at r=0 with radial scale length a. Since particle rest masses scale with S(r)/S_0, their world lines do not follow time-like geodesics of the MK metric g_ab, as previously assumed, but rather those of the Higgs-frame MK metric Omega^2 g_ab, with the conformal factor Omega(r)=S(r)/S_0. We show that the required stretching of the MK metric exactly cancels the linear potential that has been invoked to fit galaxy rotation curves without dark matter. We also formulate, for spherical structures with a Higgs halo S(r), the CG equations that must be solved for viable astrophysical tests of CG using galaxy and cluster dynamics and lensing.