Was GRB 980329 at [CLC][ITAL]z[/ITAL][/CLC] ∼ 5?

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Abstract
The optical transient (OT) associated with GRB 980329 was remarkably red. It has previously been concluded that this was the result of dust extinction in the host galaxy (Taylor et al.; Reichart et al.; Palazzi et al.). However, an extinction model can only agree with the data if the I-band observations, taken about 0.8 days after the outburst, are discounted (Klose, Meusinger, & Lehmann; Reichart et al.); the flux density ratio between the I and the R band of a factor ~7 is too great to be explained by extinction, given the relatively blue K-I color. Here it is shown that the entire observed optical/infrared spectrum is consistent with that which is expected from an unextincted OT at z~5. At this redshift, the light in the observer's R band is strongly suppressed by absorption in the Lyα forest—an effect that has been seen clearly in galaxies in the Hubble Deep Field (Weymann et al.; Spinrad et al.). In spite of its potentially high redshift, GRB 980329 was an unusually bright burst. If GRB 980329 was indeed at z~5, and its gamma rays were radiated isotropically, the implied energy of the burst would be 5 × 1054 ergs. Should GRB 980329 have a host galaxy, deep imaging could confirm or reject the conclusion that this burst was at z~5.