Emergent gravity in galaxies and in the Solar System
  It was recently proposed that the effects usually attributed to particle dark
matter on galaxy scales are due to the displacement of dark energy by baryonic
matter, a paradigm known as emergent gravity. This formalism leads to
predictions similar to Modified Newtonian Dynamics (MOND) in spherical
symmetry, but not quite identical. In particular, it leads to a well defined
transition between the Newtonian and the modified gravitational regimes, a
transition depending on both the Newtonian acceleration and its first
derivative with respect to radius. Under the hypothesis of the applicability of
this transition to aspherical systems, we investigate whether it can reproduce
observed galaxy rotation curves. We conclude that the formula leads to
marginally acceptable fits with strikingly low best-fit distances, low stellar
mass-to-light ratios, and a low Hubble constant. In particular, some unobserved
wiggles are produced in rotation curves because of the dependence of the
transition on the derivative of the Newtonian acceleration, leading, even in
the most favorable case, to systematically less good fits than MOND. Then,
applying the predicted transition from emergent gravity in a regime where it
should a priori be applicable, i.e. in spherical symmetry and outside of the
bulk of matter, we show that the predictions for the secular advances of Solar
System planets' perihelia are discrepant with the data by seven orders of
magnitude, ruling out the present emergent gravity weak-field formula with high
confidence.
