Constraints on thawing scalar field models from fundamental constants
  We consider a dark energy model with a relation between the equation of state
parameter $w$ and the energy density parameter $\Omega_\phi$ derived from
thawing scalar field models. Assuming the variation of the fine structure
constant is caused by dark energy, we use the observational data of the
variation of the fine structure constant to constrain the current value of
$w_0$ and $\Omega_{\phi 0}$ for the dark energy model. At the $1\sigma$ level,
the observational data excluded some areas around $w_0=-1$, which explains the
positive detection of the variation of the fine structure constant at the
$1\sigma$ level, but $\Lambda$CDM model is consistent with the data at the
$2\sigma$ level.
