Constraints from GRB Observation for Cosmological Models

We use Liang-Zhang relation for Gamma Ray Bursts to constrain $\Lambda $ Cold Dark Matter standard cosmology and a particular class of brane cosmology (brane-induced gravity model). With the most probable model being $\Omega _m =0.23$ and $\Omega _\Lambda =0.77$ for flat $\Lambda $CDM cosmology and $\Omega _m =0.18$ and $\Omega _{r_c } =0.17$ for flat brane-induced gravity cosmology, our result is comparable with the result from SNIa observation. With average uncertainty of distance modulus being 0.2771, the two discussed cosmologies are indistinguishable using our current sample of GRB with redshift ranging between 0.1685 and 3.2. We argue that by expanding the sample and adding more low and high redshift GRBs and also with improvement in using GRBs for cosmography, we might be able to distinguish between different cosmological models and tighten the most probable area.