Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters

TL;DR

The paper details the Planck 2015 CMB data analysis, improving data processing, foreground modeling, and polarization analysis, confirming the ΛCDM model and refining cosmological parameters with enhanced robustness and reduced uncertainties.

Contribution

It introduces improved likelihoods and foreground models for Planck 2015 data, including polarization, and validates the robustness of cosmological parameters within the ΛCDM framework.

Findings

ΛCDM model remains a good fit to data

Scalar spectral index n_s < 1 at >5σ significance

Reionization optical depth τ = 0.078 ± 0.019

Abstract

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlations of CMB data, using the hybrid approach employed previously: pixel-based at $\ell<30$ and a Gaussian approximation to the distribution of spectra at higher $\ell$. The main improvements are the use of more and better processed data and of Planck polarization data, and more detailed foreground and instrumental models, allowing further checks and enhanced immunity to systematics. Progress in foreground modelling enables a larger sky fraction. Improvements in processing and instrumental models further reduce uncertainties. For temperature, we perform an analysis of end-to-end instrumental simulations fed into the data processing pipeline; this does not reveal biases from residual instrumental systematics. The $\Lambda$CDM cosmological model continues to offer a very good fit to Planck data. The slope of primordial scalar fluctuations, $n_s$, is confirmed smaller than unity at more than 5{\sigma} from Planck alone. We further validate robustness against specific extensions to the baseline cosmology. E.g., the effective number of neutrino species remains compatible with the canonical value of 3.046. This first detailed analysis of Planck polarization concentrates on E modes. At low $\ell$ we use temperature at all frequencies and a subset of polarization. The frequency range improves CMB-foreground separation. Within the baseline model this requires a reionization optical depth $\tau=0.078\pm0.019$, significantly lower than without high-frequency data for explicit dust monitoring. At high $\ell$ we detect residual errors in E, typically O($\mu$K$^2$); we recommend temperature alone as the high-$\ell$ baseline. Nevertheless, Planck high-$\ell$ polarization allows a separate determination of $\Lambda$CDM parameters consistent with those from temperature alone.