No Evidence of Time Dilation in Gamma-Ray Burst Data

Gamma-Ray Bursts have been observed out to very high redshifts and provide time measures that are directly related to intrinsic time scales of the burst. Einstein's theory of relativity is quite definite that if the universe is expanding then the observed duration of these measures will increase with redshift. Thus gamma-ray burst measures should show a time dilation proportional to redshift. An analysis of gamma-ray burst data shows that the hypothesis of time dilation is rejected with a probability of 4.4$\times10^{-6}$ for redshifts out to z=6.6. Traditionally the lack of an apparent time dilation has been explained by an inverse correlation between luminosity and time measures together with strong luminosity selection as a function of redshift. It is shown that the inverse correlation between luminosity and some time measures is confirmed, but using concordance cosmology strong luminosity selection cannot be achieved. It may be possible to explain the apparent lack of time dilation with a combination of gamma-ray burst selection, some luminosity evolution and some time measure evolution. But this requires a remarkable coincidence in order to produce the apparent lack of time dilation. However the data are consistent with a static cosmology in a non-expanding universe.