### Abstract

The recent data release of ESA's Planck mission together with earlier Wilkinson Microwave Anisotropy Probe (WMAP) releases provide the first opportunity to compare high-resolution full sky cosmic microwave background (CMB) temperature anisotropy maps. To quantify the coherence of these maps beyond the power spectrum, we introduce Generalized Phases in the sense of SO(3), unit vectors in the 2l + 1 dimensional representation spaces. For an isotropic Gaussian distribution, Generalized Phases point to random directions and if there is non-Gaussianity, they represent most of the non-Gaussian information. The alignment of these unit vectors from two maps can be characterized by their angle, 0° expected for full coherence, and 90° for random vectors. We analyse maps from both missions with the same mask and N_{side} = 512 resolution, and compare both power spectra and Generalized Phases.We find excellent agreement of the Generalized Phases of Planck Spectral Matching Independent Component Analysis map with that of the WMAP Q, V, W maps, rejecting the null hypothesis of no correlations at 5σ for l < 700, l < 900 and l < 1100, respectively, except perhaps for l < 10. Using foreground reduced maps for WMAP increases the phase-coherence. The observed coherence angles can be explained with a simple assumption of Gaussianity and a WMAP noise model neglecting Planck noise, except for low-intermediate l values there is a slight, but significant offset, depending on the WMAP band. On the same scales WMAP power spectrum is about 2.6 per cent higher at a very high significance, while at higher l ranges there appears to be no significant bias. Using our theoretical tools, we predict the phase alignment of Planck with a hypothetical perfect noiseless CMB experiment, finding decoherence at l ≠ 2900; below this value Planck can be used most efficiently to constrain non-Gaussianity.

Original language | English |
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Pages (from-to) | 1422-1429 |

Number of pages | 8 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 436 |

Issue number | 2 |

DOIs | |

Publication status | Published - Dec 1 2013 |

### Keywords

- Cosmic background radiation-cosmology
- Cosmology
- Observations
- Theory

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Monthly Notices of the Royal Astronomical Society*,

*436*(2), 1422-1429. https://doi.org/10.1093/mnras/stt1661