Are gamma-ray bursts a standard energy reservoir?

One of the most important discoveries in the observation of gamma-ray bursts (GRBs) is that the total energy emitted by a GRB in gamma-rays has a very narrow distribution around 10(51) erg, which led people to claim that GRBs are standard energy explosions. As people made the claim they have ignored the selection biases which must be important since GRB observations are strongly fluence or flux-limited. In this paper we show that, when the selection effects are considered, the intrinsic distribution of the GRB energy can be very broad. The number of faint GRBs has been significantly underestimated because of the fluence or flux limit. The bright part of the distribution has been affected by another important selection effect arising from the beaming of GRB jets, which is instrument-independent and caused by the fact that brighter GRBs tend to have smaller jet angles and hence smaller probabilities to be detected. Our finding indicates that GRBs are not a standard energy reservoir, and challenges the proposal that GRBs can be used as standard candles to probe cosmology.