  This article studies the effects of an arbitrary dark matter spin tensor on
the propagation of gravitational wave amplitude in the context of
Einstein-Cartan theory. We choose to work with an arbitrary spin tensor
because, given our ignorance of the nature of dark matter, it is sensible not
to make further hypotheses on its spin and not to assume any particular model
for its spin tensor (or its vanishing). The analysis focuses on a
\textquotedblleft weak-torsion regime,\textquotedblright\ such that
gravitational wave emission, at leading and subleading orders, does not deviate
from standard General Relativity. We show that, in principle, the background
torsion induced by an eventual dark matter spin component could lead to an
anomalous dampening or amplification of the gravitational wave amplitude, after
going across a long cosmological distance. We assess the importance of this
torsion-induced anomalous amplitude propagation for binary black hole mergers
in a way as model-free as possible in Einstein-Cartan gravity. It is possible
to prove that at its best, for realistic late-universe cosmological scenarios,
the effect is tiny and falls below detection thresholds, even for near-future
interferometers such as LISA. Therefore, detecting this effect may not be
impossible, but it is still beyond our technological capabilities. As a
model-independent result in the Einstein-Cartan context, it also implies that
mergers are robust standard sirens without considering any potential
dark-matter-induced torsional effects.
