  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 a uniform
rotation produces in the CMB 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 CMB constraint on the rotation-angle power spectrum for multipoles
between L = 0 and L = 512. We also obtain a 68% confidence-level upper limit of
1 degree on the square root of the quadrupole of a scale-invariant
rotation-angle power spectrum.
