Estimations of the cosmological parameters from the observational variation of the fine structure constant

We present the constraints on the Quintessence scalar field model from the observational data of the variation of the fine structure constant obtained from Keck and VLT telescopes. Within the theoretical frame proposed by Bekenstein, the constraints on the parameters of the Quintessence scalar field model are obtained. By the consideration of the prior of $\Omega_{m0}$ as WMAP 7 suggests, we obtain various results of the different samples. Based on these results, we also calculate the probability density function of the coupling constant $\zeta$. The best-fit values show a consistent relationship between $\zeta$ and the different experimental results. In our work, we test two different potential models, namely, the inverse power law potential and the exponential potential. The results show that both the large value of the parameters in the potential and the strong coupling can cause the variation of fine structure constant.