Planck 2013 results. XV. CMB power spectra and likelihood
Abstract
This paper presents the Planck 2013 likelihood, a complete statistical description of the twopoint 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, ℓ, covering 2 ≤ ℓ ≤ 2500. The main source of uncertainty at ℓ ≲ 1500 is cosmic variance. Uncertainties in smallscale foreground modelling and instrumental noise dominate the error budget at higher ℓs. For ℓ < 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 ℓ ≥ 50, we employ a correlated Gaussian likelihood approximation based on a finegrained set of angular crossspectra 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 highℓ crossspectra with residuals below a few μK^{2} at ℓ ≲ 1000, in agreement with estimated calibration uncertainties. We compare our results with foregroundcleaned CMB maps derived from all Planck frequencies, as well as with crossspectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. We further show that the bestfit ΛCDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard ΛCDM cosmology is well constrained by Planck from the measurements at ℓ ≲ 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4σ deviation from scale invariance, n_{s} = 1. Increasing the multipole range beyond ℓ ≃ 1500 does not increase our accuracy for the ΛCDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the ΛCDM framework. Finally, we report a tension between the Planck bestfit ΛCDM model and the lowℓ spectrum in the form of a power deficit of 510% at ℓ ≲ 40, with a statistical significance of 2.53σ. 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.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 2014
 DOI:
 10.1051/00046361/201321573
 arXiv:
 arXiv:1303.5075
 Bibcode:
 2014A&A...571A..15P
 Keywords:

 cosmic background radiation;
 cosmological parameters;
 cosmology: observations;
 methods: data analysis;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 This paper is one of a set associated with the 2013 release of data from the Planck mission. 62 pages, 64 figures, 12 tables