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The constraints on the time variation of the fine structure constant atrecombination epoch relative to its present value, $\Delta\alpha/\alpha \equiv(\alpha_{\mathrm{rec}} - \alpha_{\mathrm{now}})/\alpha_{\mathrm{now}}$, areobtained 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 tothe analysis based on the previous WMAP data, the mean value of$\Delta\alpha/\alpha=-0.0009$ does not change significantly whether we use theHubble Space Telescope (HST) measurement of the Hubble parameter as a prior ornot. The resultant 95% confidence ranges of $\Delta\alpha/\alpha$ are $-0.028 <\Delta\alpha/\alpha < 0.026$ with HST prior and $-0.050 < \Delta\alpha/\alpha <0.042$ without HST prior.

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