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Abstract
We discuss the effect of a conformally coupled Higgs field on Conformal Gravity (CG) predictions for the rotation curves of galaxies. The MannheimKazanas (MK) metric is a valid vacuum solution of CG's 4th order Poisson equation if and 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 timelike geodesics of the MK metric g_{μν}, as previously assumed, but rather those of the Higgsframe MK metric ḡ_{μν }= Ω^{2} g_{μν}, with the conformal factor Ω(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.
Original language  English 

Pages (fromto)  41224128 
Number of pages  7 
Journal  Monthly Notices of the Royal Astronomical Society 
Volume  458 
Issue number  4 
Early online date  7 Mar 2016 
DOIs  
Publication status  Published  1 Jun 2016 
Keywords
 Gravitation
 Galaxies: kinematics and dynamics
 Cosmoslogy: theory, dark matter, dark energy
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 1 Finished

Astronomy at St Andrews 20152018: Astronomy at St Andrews 20152018
Jardine, M. M., Cameron, A. C., Cyganowski, C. J., Horne, K. D. & Wood, K.
Science & Technology Facilities Council
1/04/15 → 31/03/18
Project: Standard