Limits on anisotropic inflation from the Planck data
  Temperature anisotropy of the cosmic microwave background offers a test of
the fundamental symmetry of spacetime during cosmic inflation. Violation of
rotational symmetry yields a distinct signature in the power spectrum of
primordial fluctuations as $P({\mathbf k})=P_0(k)[1+g_*(\hat{\mathbf
k}\cdot\hat{\mathbf E}_{\rm cl})^2]$, where $\hat{\mathbf E}_{\rm cl}$ is a
preferred direction in space and $g_*$ is an amplitude. Using the
\textit{Planck} 2013 temperature maps, we find no evidence for violation of
rotational symmetry, $g_*=0.002\pm 0.016$ (68% CL), once the known effects of
asymmetry of the \textit{Planck} beams and Galactic foreground emission are
removed.
