  The exceptionally high luminosities of gamma-ray bursts (GRBs), gradually
emerging as extremely useful probes of star formation, make them promising
tools for exploration of the high-redshift Universe. Here we present a
carefully selected sample of Swift GRBs, intended to estimate in an unbiased
way the GRB mean redshift (z_mean), constraints on the fraction of
high-redshift bursts and an upper limit on the fraction of heavily obscured
afterglows. We find that z_mean = 2.8 and that at least 7% of GRBs originate at
z > 5. In addition, consistent with pre-Swift observations, at most 20% of
afterglows can be heavily obscured. The redshift distribution of the sample is
qualitatively consistent with models where the GRB rate is proportional to the
star formation rate in the Universe. We also report optical, near-infrared and
X-ray observations of the afterglow of GRB 050814, which was seen to exhibit
very red optical colours. By modelling its spectral energy distribution we find
that z = 5.3 +/- 0.3. The high mean redshift of GRBs and their wide redshift
range clearly demonstrates their suitability as efficient probes of galaxies
and the intergalactic medium over a significant fraction of the history of the
Universe.
