Limits on anisotropic inflation from the Planck data

Abstract

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 $P(\mathbf{k})=P_0(k)[1+g_{\ast }(\hat{\mathbf{k}}\cdot {\hat{\mathbf{E}}}_{\mathrm{cl}}{)}^2]$, where ${\hat{\mathbf{E}}}_{\mathrm{cl}}$ is a preferred direction in space and $g_{\ast }$ is an amplitude. Using the \textit{Planck} 2013 temperature maps, we find no evidence for violation of rotational symmetry, $g_{\ast }=0.002\pm 0.016$ (68% CL), once the known effects of asymmetry of the \textit{Planck} beams and Galactic foreground emission are removed.

5 pages, 2 figures. (v2) References added. A typo fixed. (v3) Various confidence levels included, Journal reference added (v4) error of a duplicated pdf file fixed

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