Long duration gamma-ray bursts (GRBs) allow us to explore the distant Universe, and are potentially the most effective tracer of the most distant objects. Our current knowledge of the properties of GRB host galaxies at redshifts >5 is very scarce. We propose to improve this situation by obtaining more observations of high-redshift hosts to better understand their properties and help enable us to use GRBs as probes of the high-redshift universe. We performed very deep photometric observations of three high-redshift GRB host galaxies, GRB 080913 at z =6.7, GRB 060927 at z =5.5 and GRB 060522 at z =5.1. In addition, we completed deep spectroscopic observations of the GRB080913 host galaxy with X-Shooter at the VLT to search for Ly-alpha emission. For the sake of the discussion, we use published results on another high-redshift GRB host, GRB 050904 at z = 6.3. The sample of GRB host galaxies studied in this paper consists of four out of the five spectroscopically confirmed GRBs at z>5. Despite our presented observations being the deepest ever reported of high-redshift GRB host galaxies, we do not detect any of the hosts, neither in photometry nor in spectroscopy in the case of GRB 080913. These observations indicate that the GRB host galaxies seem to evolve with time and to have lower SFRs at z >5 than they have at z<1. In addition, the host galaxy of GRB 080913 at z =6.7 does not show Ly-alpha emission. While the measured properties of the galaxies in our sample agree with the properties of the general galaxy population at z>5, our observations are not sufficiently sensitive to allow us to infer further conclusions on whether this specific population is representative of the general one. The characterization of high-redshift GRB host galaxies is a very challenging endeavor requiring a lot of telescope time, but is necessary to improve our understanding of the high-redshift universe.
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