Gamma-Ray Bursts And High-redshift Star Formation Rates:the Influence Of Gravitational Lensing

Gamma-ray bursts(GRBs for short) are suddenly enhanced gamma-ray radiation from arbitrary directions of universe in a short time. According to the duration time, GRBs are usually classified into two classes based on 2 s:Long GRBs and Short GRBs. It is widely accepted that they are respectively from collapsing massive star and results of merging compact binaries. So the rate of Long GRBs are often used to trace the cosmological evolution of star formation rate, especially high-redshift conditions. As the launch of Swift satellites, people have detected quite a few redshift of GRBs, which have laid an observation foundation for this study. On the one hand, this paper gives a detailed introduction of the construction of GRB pseudo-redshift, thus to constrain GRB luminosity function. On the other hand, this paper summarize theoretical calculation of star formation rate (including Population Ⅰ/Ⅱ and Population Ⅲ), which using collapsing model of dark matter halo. So, this paper points out that there were a large amount of dark matter halo in the universe, which may have a significant gravitational lensing effect on GRBs especially the rate of high-redshift GRBs. This will make the observed value of GRB rate higher than the proper value. In consider of this effect, we improve theoretical calculation of GRB rate, and then fit the number of pseudo-redshift GRBs again, which give a new constrain to model parameters of Population Ⅲ star formation rate, the probability of producing GRBs, and the observation efficiency of this star GRBs.