Equivalence Principle Implications of Modified Gravity Models
  Theories that attempt to explain the observed cosmic acceleration by
modifying general relativity all introduce a new scalar degree of freedom that
is active on large scales, but is screened on small scales to match
experiments. We show that if such screening occurrs via the chameleon mechanism
such as in f(R), it is possible to have order one violation of the equivalence
principle, despite the absence of explicit violation in the microscopic action.
Namely, extended objects such as galaxies or constituents thereof do not all
fall at the same rate. The chameleon mechanism can screen the scalar charge for
large objects but not for small ones (large/small is defined by the
gravitational potential and controlled by the scalar coupling). This leads to
order one fluctuations in the inertial to gravitational mass ratio. In Jordan
frame, it is no longer true that all objects move on geodesics. In contrast, if
the scalar screening occurrs via strong coupling, such as in the DGP braneworld
model, equivalence principle violation occurrs at a much reduced level. We
propose several observational tests of the chameleon mechanism: 1. small
galaxies should fall faster than large galaxies, even when dynamical friction
is negligible; 2. voids defined by small galaxies would be larger compared to
standard expectations; 3. stars and diffuse gas in small galaxies should have
different velocities, even on the same orbits; 4. lensing and dynamical mass
estimates should agree for large galaxies but disagree for small ones. We
discuss possible pitfalls in some of these tests. The cleanest is the third one
where mass estimate from HI rotational velocity could exceed that from stars by
30 % or more. To avoid blanket screening of all objects, the most promising
place to look is in voids.
