Cosmological Evolution of Long Gamma-ray Bursts and Star Formation Rate
  Gamma-ray bursts (GRBs) by virtue of their high luminosities can be detected
up to very high redshifts and therefore can be excellent probes of the early
universe. This task is hampered by the fact that most of their characteristics
have a broad range so that we first need to obtain an accurate description of
the distribution of these characteristics, and specially, their cosmological
evolution. We use a sample of about 200 \swift long GRBs with known redshift to
determine the luminosity and formation rate evolutions and the general shape of
the luminosity function. In contrast to most other forward fitting methods of
treating this problem we use the Efron Petrosian methods which allow a
non-parametric determination of above quantities. We find a relatively strong
luminosity evolution, a luminosity function that can be fitted to a broken
power law, and an unusually high rate of formation rate at low redshifts, a
rate more than one order of magnitude higher than the star formation rate
(SFR). On the other hand, our results seem to agree with the almost constant
SFR in redshifts 1 to 3 and the decline above this redshift.
