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.

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