Cosmological Constraints on the Gravitational Interactions of Matter and
  Dark Matter
  Although there is overwhelming evidence of dark matter from its gravitational
interaction, we still do not know its precise gravitational interaction
strength or whether it obeys the equivalence principle. Using the latest
available cosmological data and working within the framework of
$\Lambda\mbox{CDM}$, we first update the measurement of the Newton's constant
for all matter: $G_N=7.26^{+0.27}_{-0.27}\times
10^{-11}\,\mbox{m}^{3}\mbox{kg}^{-1}\mbox{s}^{-2}$, which differs by $2.2
\sigma$ from the standard laboratory-based value. In general relativity, dark
matter equivalence principle breaking can be mimicked by a long-range dark
matter force mediated by an ultra light scalar field. Using the Planck three
year data, we find that the dark matter "fifth-force" strength is constrained
to be weaker than $10^{-4}$ of the gravitational force. We also introduce a
phenomenological, post-Newtonian two-fluid description to explicitly break the
equivalence principle by introducing a difference between dark matter inertial
and gravitational masses. Depending on the decoupling time of the dark matter
and ordinary matter fluids, the ratio of the dark matter gravitational mass to
inertial mass is constrained to be unity at the $10^{-6}$ level.
