### Abstract

This paper presents the Planck 2013 likelihood, a
complete statistical description of the two-point
correlation function of the CMB temperature fluctuations
that accounts for all known relevant uncertainties, both
instrumental and astrophysical in nature. We use this
likelihood to derive our best estimate of the CMB angular
power spectrum from Planck over three decades in
multipole moment, covering 22500. The main source of
uncertainty at 1500 is cosmic variance. Uncertainties in
small-scale foreground modelling and instrumental noise
dominate the error budget at higher s. For <50, our
likelihood exploits all Planck frequency channels from 30
to 353 GHz, separating the cosmological CMB signal from
diffuse Galactic foregrounds through a physically
motivated Bayesian component separation technique. At 50,
we employ a correlated Gaussian likelihood approximation
based on a fine-grained set of angular cross-spectra
derived from multiple detector combinations between the
100, 143, and 217 GHz frequency channels, marginalising
over power spectrum foreground templates. We validate our
likelihood through an extensive suite of consistency
tests, and assess the impact of residual foreground and
instrumental uncertainties on the final cosmological
parameters. We find good internal agreement among the
high-cross-spectra with residuals below a few K2 at 1000,
in agreement with estimated calibration uncertainties. We
compare our results with foreground-cleaned CMB maps
derived from all Planck frequencies, as well as with
cross-spectra derived from the 70 GHz Planck map, and
find broad agreement in terms of spectrum residuals and
cosmological parameters. We further show that the
best-fit CDM cosmology is in excellent agreement with
preliminary PlanckEE and TE polarisation spectra. We find
that the standard CDM cosmology is well constrained by
Planck from the measurements at 1500. One specific
example is the spectral index of scalar perturbations,
for which we report a 5.4 deviation from scale
invariance, n= 1. Increasingthe multipole range beyond
1500 does not increase our accuracy for the CDM
parameters, but instead allows us to study extensions
beyond the standard model. We find no indication of
significant departures from the CDM framework. Finally,
we report a tension between the Planck best-fit CDM model
and the low-spectrum in the form of a power deficit of
510% at 40, with a statistical significance of 2.53.
Without a theoretically motivated model for this power
deficit, we do not elaborate further on its cosmological
implications, but note that this is our most puzzling
finding in an otherwise remarkably consistent data set.

Original language | English |
---|---|

Article number | A15 |

Number of pages | 62 |

Journal | Astronomy and Astrophysics |

Volume | 571 |

DOIs | |

Publication status | Published - 2014 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- cosmic background radiation
- cosmological parameters
- cosmology
- data analysis

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## Cite this

Varis, J., Tuovinen, J., & Planck Collaboration (2014). Planck 2013 results. XV. CMB power spectra and likelihood.

*Astronomy and Astrophysics*,*571*, [A15]. https://doi.org/10.1051/0004-6361/201321573