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Gamma-ray bursts (GRBs) by virtue of their high luminosities can be detectedup to very high redshifts and therefore can be excellent probes of the earlyuniverse. This task is hampered by the fact that most of their characteristicshave a broad range so that we first need to obtain an accurate description ofthe distribution of these characteristics, and specially, their cosmologicalevolution. We use a sample of about 200 \swift long GRBs with known redshift todetermine the luminosity and formation rate evolutions and the general shape ofthe luminosity function. In contrast to most other forward fitting methods oftreating this problem we use the Efron Petrosian methods which allow anon-parametric determination of above quantities. We find a relatively strongluminosity evolution, a luminosity function that can be fitted to a brokenpower law, and an unusually high rate of formation rate at low redshifts, arate 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 constantSFR in redshifts 1 to 3 and the decline above this redshift.

Cosmological Evolution of Long Gamma-ray Bursts and Star Formation Rate