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.