Testing Gravity with Gravitational Wave Source Counts
  We show that the gravitational wave source counts distribution can test how
gravitational radiation propagates on cosmological scales. This test does not
require obtaining redshifts for the sources. If the signal-to-noise ratio (SNR,
$\rho$) from a gravitational wave source is proportional to the strain then it
falls as $R^{-1}$, thus we expect the source counts to follow $dN/d\rho \propto
\rho^{-4}$. However, if gravitational waves decay as they propagate or
propagate into other dimensions, then there can be deviations from this generic
prediction. We consider the possibility that the strain falls as $R^{-\gamma}$,
where $\gamma=1$ recovers the expected predictions in a Euclidean
uniformly-filled universe, and forecast the sensitivity of future observations
to deviations from standard General Relativity. We first consider the case of
few objects, 7 sources, with a signal-to-noise from 8 to 24, and impose a lower
limit on $\gamma$, finding $\gamma>0.33$ at $95\%$ confidence level. The
distribution of our simulated sample is very consistent with the distribution
of the trigger events reported by Advanced LIGO. Future measurements will
improve these constraints: with 100 events, we estimate that $\gamma$ can be
measured with an uncertainty of $15\%$. We generalize the formalism to account
for a range of chirp masses and the possibility that the signal falls as
$\exp(-R/R_0)/R^\gamma$.
