The Distance of GRB is Independent from the Redshift
  Although it is acknowledged that GRB redshift is cosmological at present, but it in fact has never been confirmed. However, the fact is still unclear because which may be cosmological redshift (including possibly the host galaxy redshift or the background galaxy redshift) or the redshift results from gravity of neutron star; in other words, GRB redshift may be related to its distance or not. Here, I enumerate a series of evidences, including three methods, to determine whether the GRB distance does depend on the redshift. Firstly, the correlation analysis shows that there is no correlation between the fluence of 131 GRBs (and the 1 s peak photon flux of 111 GRBs) and the redshift although there is a significant correlation between the apparent magnitude of 32 hosts and the redshift. Secondly, from the number-redshift relation of GRBs and the deductive reasoning, one can deduce an absurd conclusion that the probability of a nearby galaxy generating a GRB event would vary inversely as its distance square if GRB indeed comes from an external galaxy and the distance depends on the redshift. Thirdly, if the distance is related to the redshift, then the variables of fluence and peak flux definitely cannot be separated from the variable of redshift in distribution functions of both the fluence-redshift and the peak flux-redshift; while the variables separation tests show that they in effect do, and we then can exactly forecast the values of the fluence and the peak flux for the GRBs with redshift z > 4.5. Other evidences all show that GRB distance is independent from the redshift without exception. 
Fu-gao Song