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. 
Qing Gao and Yungui Gong
astro-ph.CO gr-qc hep-th