**10. Further Application of GRBs as Probes of the High-Redshift Universe**

Above, we faced some of the standard statistical methods associated with GRBs, and we proposed a few applications with the corresponding experimental bounds. Now

we shortly review other phenomenological applications of GRBs that can shed light on the high-redshift Universe.

#### *10.1. Star Formation Rate from GRBs*

LGRBs are likely associated with core-collapse SNe [38,230]. By virtue of this fact, GRB-SN associations may provide a complementary technique that measures a high-redshift star formation rate [231–235]. Again, a problem related to calibration occurs, i.e., how to calibrate a GRB event rate with a star formation rate. Moreover, the luminosity function is not known a priori, and its reconstruction depends on the particular model selected for the analysis [236–239]. The typical functional structures for the luminosity functions are (i) a broken power law [240] and (ii) a single power law with an exponential cut-off at low luminosities [237]. Reconstructed SFRs from GRBs are typically larger than those from other observations [241]. The reason behind this apparent inconsistency may reside in the fact that usually SFR at high-*z* is obtained from the observations of the brightest galaxies, whereas GRBs, in view of their high luminosities, may help in detecting faint galaxies at high-*z* otherwise unobserved [241,242].
