  The cosmological origin of cosmic gamma-ray bursts is tested using the method
of peak alignment for the averaging of time profiles. The test is applied to
the basic cosmological model with standard sources, which postulates that
difference between bright and dim bursts results from different cosmological
red-shifts of their sources. The average emissivity curve (ACEbright) of the
group of bright BATSE bursts is approximated by a simple analytical function,
which takes into account the effect of squeezing of the time pulses with
increasing energy of photons. This function is used to build the model light
curve for ACEdim of dim BATSE bursts, which takes into account both the
cosmological time- stretching of bursts light curves and the red-shifting of
photons energies. Direct comparison between the model light curve and the
ACEdim of dim bursts is performed, which is based on the estimated
probabilities of differences between ACEs of randomly selected groups of
bursts. It shows no evidence for the predicted cosmological effects. The 3
sigma upper limit of the average red- shift Zdim of emitters of dim bursts is
estimated to be as small, as 0.1-0.5, which is not consistent with values 1
predicted by the known cosmological models of gamma-ray bursts.
