  The Lambda-Cold Dark Matter model explains cosmological observations most
accurately till date. However, it is still plagued with various shortcomings at
galactic scales. Models of dark matter such as superfluid dark matter,
Bose-Einstein Condensate(BEC) dark matter and fuzzy dark matter have been
proposed to overcome some of these drawbacks. In this work, we probe these
models using the current constraint on the gravitational wave (GW) propagation
speed coming from the binary neutron star GW170817 detection by LIGO-Virgo
detector network and use it to study the allowed parameter space for these
three models for Advanced LIGO+Virgo, LISA, IPTA and SKA detection frequencies.
The speed of GW has been shown to depend upon the refractive index of the
medium, which in turn, depends on the dark matter model parameters through the
density profile of the galactic halo. We constrain the parameter space for
these models using the bounds coming from GW speed measurement and the Milky
Way radius bound. Our findings suggest that with Advanced LIGO-Virgo detector
sensitivity, the three models considered here remain unconstrained. A
meaningful constraint can only be obtained for detection frequencies $\leq
10^{-9}$ Hz, which falls in the detection range of radio telescopes such as
IPTA and SKA. Considering this best possible case, we find that out of the
three condensate models, the fuzzy dark matter model is the most feasible
scenario to be falsified/ validated in near future.
