First CMB constraints on direction-dependent cosmological birefringence from WMAP-7

Abstract

A Chern-Simons coupling of a new scalar field to electromagnetism may give rise to cosmological birefringence, a rotation of the linear polarization of electromagnetic waves as they propagate over cosmological distances. Prior work has sought this rotation, assuming the rotation angle to be uniform across the sky, by looking for the parity-violating $TB$ and $EB$ correlations that a uniform rotation produces in the cosmic microwave background temperature/polarization. However, if the scalar field that gives rise to cosmological birefringence has spatial fluctuations, then the rotation angle may vary across the sky. Here we search for direction-dependent cosmological birefringence in the WMAP-7 data. We report the first cosmic microwave background constraint on the rotation-angle power spectrum ${C}_{L}^{\ensuremath{\alpha}\ensuremath{\alpha}}$ for multipoles between $L=0$ and $L=512$. We also obtain a 68% confidence-level upper limit of $\sqrt{{C}_{2}^{\ensuremath{\alpha}\ensuremath{\alpha}}/(4\ensuremath{\pi})}\ensuremath{\lesssim}1\ifmmode^\circ\else\textdegree\fi{}$ on the quadrupole of a scale-invariant rotation-angle power spectrum.