Measuring α in the early Universe:: cosmic microwave background polarization, re-ionization and the Fisher matrix analysis

We present a detailed analysis of present and future cosmic microwave background (CMB) constraints of the value of the fine-structure constant, alpha. We carry out a more detailed analysis of the WMAP first-year data, deriving state-of-the-art constraints on alpha and discussing various other issues, such as the possible hints for the running of the spectral index. We find, at 95 per cent confidence level, that 0.95