Together with the observed high-energy properties, an extragalactic origin for GRBs has profound implications for their origin, an issue known as the "compactness" problem \cite{Ruderman_1975}.  Specifically, the optical depth to electron-positron pair production in such a system should be extremely large, inconsistent with the non-thermal spectra observed out to several MeV.  The solution to this problem, first identified by Bohdan Paczynski \cite{Paczynski_1986} was to invoke ultra-relativistic expansion.  Specifically, Lorentz factors in excess of 100 (the most relativistic known sources in the Universe) are required in order to circumvent the compactness problem.

Excercise 1: Calculate the optical depth to electron-positron pair production for a cosmological GRB, both in the case of a static system and for relativistically expanding ejecta.