Measuring $\hat{I}\pm$ 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, $\hat{I}\pm$. We carry out a more detailed analysis of the WMAP first-year data, deriving state-of-the-art constraints on $\hat{I}\pm$ and discussing various other issues, such as the possible hints for the running of the spectral index. We find, at 95% C.L. that $0.95<\hat{I}{\pm }_{\text{dec}}/\hat{I}{\pm }_0<1.02$. Setting $d{n}_S/dlnk=0$, yields $0.94<\hat{I}{\pm }_{\text{dec}}/\hat{I}{\pm }_0<1.01$ as previously reported. We find that a lower value of $\hat{I}\pm /\hat{I}{\pm }_0$ 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 $\hat{I}\pm$ and the optical depth $\ddot{I}„$), in order to estimate how future CMB experiments will be able to constrain $\hat{I}\pm$ and other cosmological parameters. We find that Planck data alone can constrain $\ddot{I}„$ 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 $\hat{I}\pm$ 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.

29 pages, 11 figures, 15 tables, submitted to MNRAS. Higher resolution figures available at http://www.mrao.cam.ac.uk/~graca/alpha