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

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

2003-09-08

arxiv.org/abs/astro-ph/0309211v1

Mon.Not.Roy.Astron.Soc.352:20,2004

Astronomy and Astrophysics

Astrophysics

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

Scientific paper

10.1111/j.1365-2966.2004.07832.x

We present a detailed analysis of present and future Cosmic Microwave Background 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% C.L. that $0.95 < \alpha_{\text{dec}} / \alpha_0 < 1.02$. Setting $dn_S /dlnk=0$, yields $0.94< \alpha_{\text{dec}} / \alpha_0 < 1.01$ as previously reported. We find that a lower value of $\alpha / \alpha_0$ 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 $\alpha$ and the optical depth $\tau$), in order to estimate how future CMB experiments will be able to constrain $\alpha$ and other cosmological parameters. We find that Planck data alone can constrain $\tau$ 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 $\alpha$ 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.

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