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

TL;DR

This paper investigates how spatial variations in the fine structure constant, caused by a scalar field coupled to electromagnetism, affect the cosmic microwave background's temperature and polarization power spectra.

Contribution

It demonstrates that scalar field fluctuations can generate new temperature anisotropies and induce B-mode polarization in the CMB.

Findings

Scalar field fluctuations modify CMB power spectra.

New temperature anisotropies are generated at linear order.

B-mode polarization is induced at higher order.

Abstract

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.