## Spacetime variation of $\alpha$ and the CMB power spectra after the recombination

Wang, Xiulian
Li, Mingzhe
##### Description
The possible variation of the fine structure constant may be due to the non-minimal coupling of the electromagnetic field to a light scalar field which can be the candidate of dark energy. Its dynamical nature renders the fine structure constant varies with time as well as space. In this paper we point out the spatial fluctuation of the fine structure will modify the power spectra of the temperature and the polarization of the cosmic microwave background. We show explicitly that the fluctuations of the coupled scalar field generate new temperature anisotropies at the linear order and induce a $B$ mode to the polarization at higher order in general.
Comment: 7 pages; references added, typos corrected
##### Keywords
Astrophysics - Cosmology and Nongalactic Astrophysics, General Relativity and Quantum Cosmology, High Energy Physics - Phenomenology