  Motivated by the recent breakthrough of the detection of Gravitational Waves
(GW) from coalescent black holes by the aLIGO interferometers, we study the
propagation of GW in the {\sl D-material universe}, which we have recently
shown to be compatible with large-scale structure and inflationary
phenomenology. The medium of D-particles induces an effective mass for the
graviton, as a consequence of the formation of recoil-velocity field
condensates due to the underlying Born-Infeld dynamics. There is a competing
effect, due to a super-luminal refractive index, as a result of the
gravitational energy of D-particles acting as a dark matter component, with
which propagating gravitons interact. We examine conditions for the condensate
under which the latter effect is sub-leading. We argue that if quantum
fluctuations of the recoil velocity are relatively strong, which can happen in
the current era of the universe, then the condensate, and hence the induced
mass of the graviton, can be several orders of magnitude larger than the
magnitude of the cosmological constant today. Hence, we constrain the graviton
mass using aLIGO and pulsar timing observations (which give the most stringent
bounds at present). In such a sub-luminal graviton case, there is also a
gravitational Cherenkov effect for ordinary high energy cosmic matter, which is
further constrained by means of ultra-high-energy cosmic ray observations.
Assuming cosmic rays of extragalactic origin, the bounds on the quantum
condensate strength, based on the gravitational Cherenkov effect, are of the
same order as those from aLIGO measurements, in contrast to the case where a
galactic origin of the cosmic rays is assumed, in which case the corresponding
bounds are much weaker.
