Measuring $α$ in the Early Universe: CMB Polarization, Reionization and the Fisher Matrix Analysis

Abstract

We present a detailed analysis of present and future Cosmic Microwave Background constraints of the value of the fine-structure constant, $α$. We carry out a more detailed analysis of the WMAP first-year data, deriving state-of-the-art constraints on $α$ and discussing various other issues, such as the possible hints for the running of the spectral index. We find, at 95% C.L. that $0.95 < α_{\text{dec}} / α_0 < 1.02$. Setting $dn_S /dlnk=0$, yields $0.94< α_{\text{dec}} / α_0 < 1.01$ as previously reported. We find that a lower value of $α/ α_0$ makes a value of $d n_S /dlnk = 0$ more compatible with the data. We also perform a thorough Fisher Matrix Analysis (including both temperature and polarization, as well as $α$ and the optical depth $τ$), in order to estimate how future CMB experiments will be able to constrain $α$ and other cosmological parameters. We find that Planck data alone can constrain $τ$ with a accuracy of the order 4% and that this constraint can be as small as 1.7% for an ideal cosmic variance limited experiment. Constraints on $α$ are of the order 0.3% for Planck and can in principle be as small as 0.1% using CMB data alone - tighter constraints will require further (non-CMB) priors.