WMAP Constraints on varying $\alpha$ and the Promise of Reionization

Abstract

We present up-to-date constraints on the value of the fine-structure constant at the epoch of decoupling from the recent observations made by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. In the framework of models we considered, a positive (negative) variation of the value of $\alpha$ at decoupling with respect to the present-day value is now bounded to be smaller than 2% (6%) at 95% confidence level. We point out that the existence of an early reionization epoch as suggested by the above measurements will, when more accurate cosmic microwave background polarization data is available, lead to considerably tighter constraints. The so-called `reionization bump', in particular, will be extremely useful for this purpose. We find that constraints on $\alpha$ can in principle only be as small as $0.1 %$ using CMB data alone--tighter constraints will require further (non-CMB) priors.