Cosmological GRBs seem to be a relatively homogeneous population of sources with a narrow luminosity function (the peak luminosity of GRBs varies by less than a factor of 10 [183, 186]) that is located at relatively high redshifts [56, 302, 303, 304, 183]. The universe and our Galaxy are transparent to MeV -rays (see e.g. ). Hence GRBs constitute a unique homogeneous population of sources which does not suffer from any angular distortion due to absorption by the Galaxy or by any other object. Could GRBs be the holy grail of Cosmology and provide us with the standard candles needed to determine the cosmological parameters H0, , and ? Lacking any spectral feature, there is no indication of the redshift of individual bursts. The available number vs. peak luminosity distribution is is not suitable to distinguish between different cosmological models even when the sources are perfect standard candles with no source evolution .
The situation might be different if optical afterglow observations would yield an independent redshift measurement of a large number of bursts. If the GRB luminosity function is narrow enough this might allow us, in the future, to determine the cosmological closure parameter using a peak-flux vs. red-shift diagram (or the equivalent more common magnitude - red-shift diagram). For example a hundred bursts with a measured z are needed to estimate with an accuracy of = 0.2, if L / L = 1 .
Currently, the rate of detection of bursts with counter-parts is a few per year and of those detected until now only two have a measured red-shift. This rate is far too low for any cosmological measurement. However, there is an enormous potential for improvements. For example, systematic measurements of the red-shift of all bursts observed by BATSE ( 300 per year) would yield an independent estimate of , with = 0.1, even if the luminosity function is wide, (L / L = 0.9), within one year.
Direct redshift measurements would also enable us to determine the cosmological evolution of the rate of GRBs . Most current cosmological GRB models suggest that the GRB rate follows (with a rather short time delay) the rate of star formation . Consequently measurements of the rate of GRBs as a function of the red-shift will provide an independent tool to study star formation and galactic evolution.
It is also expected that the bursts' sources follow the matter distribution. Then GRBs can map the large scale structure of the Universe on scales that cannot be spanned directly otherwise. Lamb & Quashnock  have pointed out that a population of several thousand cosmological bursts should show angular deviations from isotropy on a scale of a few degrees. This would immediately lead to new interesting cosmological limits. So far there is no detected anisotropy in the 1112 bursts of the BATSE 3B catalog . But the potential of this population is clear and quite promising. A more ambitious project would be to measure the multipole moments of the GRB distribution and from this to estimate cosmological parameters . However, it seems that too many bursts are required to overcome the signal to noise ratio in such measurements.
GRBs can also serve to explore cosmology as a background population which could be lensed by foreground objects . While standard gravitational lensed object appears as several images of the same objects, the low angular resolution of GRB detectors is insufficient to distinguish between the positions of different images of a lensed GRB. However, the time delay along the different lines of sight of a gravitationally lensed burst will cause such a burst to appear as repeated bursts with the same time profile but different intensities from practically the same position on the sky. Mao  estimated that the probability for lensing of a GRB by a regular foreground galaxy is 0.04%-0.4%. Hence the lack of a confirmed lensed event so far  is not problematic yet. In the future, the statistics of lensed bursts could probe the nature of the lensing objects and the dark matter of the Universe . The fact that no lensed bursts have been detected so far is sufficient to rule out a critical density ( = 1) of 106.5 M to 108.1 M black holes . Truly, this was not the leading candidate for cosmological dark matter. Still this result is a demonstration of the power of this technique and the potential of GRB lensing. The statistics of lensing depends on the distance to the lensed objects which is quite uncertain at present. The detection of a significant number of counterparts whose red-shift could be measured would improve significantly this technique as well.