For GRBs at cosmological distances, only some 30+ redshifts have determined.
For the other 3000+ GRB that have been detected in gamma-rays, one of
the few options available for gleaning information on the distance
is the use of the brightness distribution, i.e. the number of sources
with peak flux greater than a certain value, log N(>F) vs. log F. This
distribution is expected to have a slope of -3/2 in the brightness
limited Euclidean case, and is observed to have that only at the brighter
end, flattening at the fainter end to something that appears to be -0.9
or so. This could be due either to cosmological redshift effects, or
to having reached a limiting maximum redshift, or may be due to having
reached a maximum redshift plus having a luminosity function of slope
which reproduces the low-brightness slope. Other methods for testing
GRB redshift distributions are discussed here.
Work on GRB cosmology has been going on in collaboration with Attila Meszaros
(no relation; from Charles University, Prague), Istvan Horvath (Bolyai University,
Budapest), Daniel Reichart (B.S., Penn State, now U. North Carolina), and
L. Balazs (Konkoly Observatory, Budapest); as well as Prof. Tom Abel (Penn State)
and Mr. Li Jun Gou (Penn State).
Other related work at Penn State on gamma-ray burst physics is found by clicking on this link.
``Gamma-ray bursts as X-ray depth-gauges of the Universe", Meszaros, P & Rees, M.J., 2003, Ap.J.(Lett.), 591, L91 (astro-ph/0305115)
``Detectability of Long GRB Afterglows from Very High Redshifts", Gou L.J., Meszaros, P., Abel, T. & Zhang, B., 2003, Ap.J., subm (astro-ph/0307489)
``Gamma Photometric Redshifts for Long Gamma-Ray Bursts", Bagoly Z, Csabai I, Meszaros A, Meszaros P, Horvath I, Balazs LG & Vavrek R, 2003, Astron.Ap., 398, 919 (astro-ph/0211539)
``Constraint on the Redshift and Luminosity Distributions of Gamma-Ray Bursts in an Einstein-de Sitter Universe", Reichart. D.E. & Meszaros, P., 1997, Ap.J., 483, 597
``A Principal Component Analysis of the 3B Gamma-Ray Burst Data", Bagoly, Z, Meszaros, A, Horvath, I, Balazs, L & Meszaros, P, 1998, Ap.J., 498, 342
``Cosmological Evolution and Luminosity Function Effects on Number Counts, Redshift and Time Dilation of Bursting Sources", Meszaros, A. and Meszaros, P., 1996, Ap.J., 466, 29.
``Cosmological Brightness Distribution Fits of Gamma Ray Burst Sources", Horvath, I., Meszaros, P. and Meszaros, A., 1996, Ap.J., 470, 56
`A New Proof of the Cosmological Origin of the Gamma Ray Bursts", Meszaros, A., Meszaros, P, Horvath, I, and Bagoly, Z., (1996), J. Korean Astron. Soc.. 29, S43
``The Brightness Distribution of Gamma-ray Bursters in Relativistic Cosmologies", Meszaros, P. and Meszaros, A., 1995, Ap.J., 449, 9.