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.
