Future generations of gravitational wave detectors will have the sensitivity to detect gravitational wave events at redshifts far beyond any detectable electromagnetic sources. We show that if the observed event rate is greater than one event per year at redshifts z≥40, then the probability distribution of primordial density fluctuations must be significantly non-Gaussian or the events originate from primordial black holes. The nature of the excess events can be determined from the redshift distribution of the merger rate.