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. [305]).
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
[183].
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
[201].
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 [201]. Most current cosmological GRB models suggest that the GRB rate follows (with a rather short time delay) the rate of star formation [306]. 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 [307] 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 [308]. 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 [58]. 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
[53]. 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
[309]
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
[310]
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
[54].
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 [55].
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.