### Abstract

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 |

### Fingerprint

### Keywords

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

### Cite this

*Astronomy and Astrophysics*,

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

}

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

**Planck 2013 results. XV. CMB power spectra and likelihood.** / Varis, Jussi; Tuovinen, Jussi; Planck Collaboration.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Planck 2013 results.

T2 - XV. CMB power spectra and likelihood

AU - Varis, Jussi

AU - Tuovinen, Jussi

AU - Planck Collaboration

N1 - Project code: 18080

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - cosmic background radiation

KW - cosmological parameters

KW - cosmology

KW - data analysis

U2 - 10.1051/0004-6361/201321573

DO - 10.1051/0004-6361/201321573

M3 - Article

VL - 571

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

M1 - A15

ER -