  Gravitational wave astronomy has placed strong constraints on fundamental
physics, and there is every expectation that future observations will continue
to do so. In this work we quantify this expectation for future binary merger
observations to constrain hidden sectors, such as scalar-tensor gravity or dark
matter, which induce a Yukawa-type modification to the gravitational potential.
We explicitly compute the gravitational waveform, and perform a Fisher
information matrix analysis to estimate the sensitivity of next generation
gravitational wave detectors to these modifications. We find an optimal
sensitivity to the Yukawa interaction strength of $10^{-5}$ and to the
associated dipole emission parameter of $10^{-7}$, with the best constraints
arising from the Einstein Telescope. When applied to a minimal model of dark
matter, this provides an exquisite probe of dark matter accumulation by neutron
stars, and for sub-TeV dark matter gravitational waves are able to detect mass
fractions $m_{DM}/m_{NS}$ less then 1 part in $10^{15}$.
