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It has been shown that the observed temporal distribution of transient eventsin the cosmos can be used to constrain their rate density. Here we show thatthe peak flux--observation time relation takes the form of a power law that isinvariant to the luminosity distribution of the sources, and that the methodcan be greatly improved by invoking time reversal invariance and the temporalcosmological principle. We demonstrate how the method can be used to constraindistributions of transient events, by applying it to Swift gamma-ray burst dataand show that the peak flux--observation time relation is in good agreementwith recent estimates of source parameters. We additionally show that theintrinsic time dependence allows the method to be used as a predictive tool.Within the next year of Swift observation, we find a 50% chance of obtaining apeak flux greater than that of GRB 060017 -- the highest Swift peak flux todate -- and the same probability of detecting a burst with peak flux > 100photons s^{-1} cm^{-2} within 6 years.

An improved method for estimating source densities using the temporal distribution of Cosmological Transients