# Mannheim's conformal gravity vs Dark Matter

1. Jun 27, 2013

### nicoo

I have recently been quite impressed by Mannheim's work on Conformal Gravity.
He claims to reproduce the rotation of a sample of 141 galaxies without any need of Dark Matter. In particular, in 1211.0188 its predictions seem to match extremely well to the experimental data.

Galactic rotation curves in conformal gravity
Philip D. Mannheim, James G. O'Brien
http://arxiv.org/abs/1211.0188
We review some recent work by Mannheim and O'Brien on the systematics of galactic rotation curves in the conformal gravity theory. In this work the conformal theory was applied to a comprehensive, high quality sample of spiral galaxies whose rotation curves extend well beyond the galactic optical disks. On galactic scales the conformal gravitational theory departs from the standard Newtonian theory in two distinct ways. One is a local way in which local matter sources within galaxies generate not just Newtonian potentials but linear potentials as well. The other is a global way in which two universal global potentials, one linear the other quadratic, are generated by the rest of the matter in the universe. The study involves a broad set of 138 spiral galaxies of differing luminosities and sizes, and is augmented here through the inclusion of an additional three tidal dwarf galaxies. With its linear and quadratic potentials the conformal theory can account for the systematics of an entire 141 galaxy sample without any need for galactic dark matter, doing so with only one free parameter per galaxy, namely the visible galactic mass to light ratio.

Last week, a paper was published claiming to refute Mannheim's program.

Falsification of Mannheim's conformal gravity program
Youngsub Yoon
http://arxiv.org/abs/1305.0163
We show that Mannheim's conformal gravity program, whose potential has a term proportional to $1/r$ and another term proportional to $r$, doesn't reduce to Newtonian gravity at short distances. Therefore, despite the claim that it successfully explains galaxy rotation curves, it seems falsified by numerous Cavendish-type experiments performed at laboratories on Earth whose work haven't found any deviations from Newton's theory. Moreover, it can be shown that as long as the total mass of proton is positive, Mannheim's conformal gravity program leads to negative linear potential which is undesirable from the point of view of fitting galaxy rotation curve, which necessarily requires positive linear potential

Is really Mannheim's Conformal Gravity (as it is) refuted by experiment ?
Any opinion about Yoon's paper ?