Constraints on the time variation of the fine structure constant by the 5-year WMAP data

The constraints on the time variation of the fine structure constant at recombination epoch relative to its present value, $\Delta\alpha/\alpha \equiv (\alpha_{$\mathrm{r}\mathrm{e}\mathrm{c}$} - \alpha_{$\mathrm{n}\mathrm{o}\mathrm{w}$})/\alpha_{$\mathrm{n}\mathrm{o}\mathrm{w}$}$, are obtained from the analysis of the 5-year WMAP cosmic microwave background data. As a result of Markov-Chain Monte-Carlo analysis, it is found that, contrary to the analysis based on the previous WMAP data, the mean value of $\mathrm{\Delta }\alpha \mathrm{/}\alpha =-0.0009$ does not change significantly whether we use the Hubble Space Telescope (HST) measurement of the Hubble parameter as a prior or not. The resultant 95% confidence ranges of $\mathrm{\Delta }\alpha \mathrm{/}\alpha$ are $-0.028 < \Delta\alpha/\alpha < 0.026$withHSTpriorand$-0.050 < \Delta\alpha/\alpha < 0.042$ without HST prior.