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 $P({\mathbf k})=P_0(k)[1+g_*(\hat{\mathbf k}\cdot\hat{\mathbf E}_{\rm cl})^2]$, 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.

Figures (2)

• Figure 1: (Left) The Planck temperature map at 143 GHz. (Middle) The foreground-reduced map at 143 GHz. (Right) The foreground mask. The maps are shown in a Mollweide projection in Galactic coordinates.
• Figure 2: (Left) Log-likelihood of locations of a preferred direction, $\ln \mathcal{L}(\hat{\mathbf E}_{\mathrm{cl}})$, computed from the foreground-reduced map at 143 GHz. (Middle) $\ln \mathcal{L}(\hat{\mathbf E}_{\mathrm{cl}})$ from the average of simulations with the asymmetric beam. There are two peaks due to parity symmetry. The peaks lie close to the Ecliptic pole. The over-laid grids show Ecliptic coordinates. (Right) $\ln \mathcal{L}(\hat{\mathbf E}_{\mathrm{cl}})$ after removing the mean field due to the asymmetric beam. No obvious peaks are left.