Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters (1507.02704v3)

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.

• The paper demonstrates how robust likelihood frameworks extract precise ΛCDM parameters from extensive CMB power spectra data.
• The analysis employs specialized methods for both low and high multipole regions, addressing cosmic variance and acoustic complexities.
• The results reinforce the standard cosmological model while highlighting tensions in parameters that motivate future research.

Planck 2015 Results: CMB Power Spectra and Cosmological Analysis

The paper "Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters" presents an in-depth analysis of the cosmic microwave background (CMB) data acquired by the Planck satellite. This research focuses on the CMB power spectra, the likelihood framework utilized for parameter estimation, and evaluates the robustness of the resultant cosmological parameters. The Planck mission has been instrumental in refining our understanding of cosmology, providing pivotal data on the early universe's characteristics.

Overview of Methodology

The paper employs a comprehensive approach to analyze the CMB power spectra, covering both low and high multipole moments (ℓ) regions. The likelihood framework, a crucial aspect of interpreting the raw Planck data, is meticulously developed to derive constraints on the cosmological model parameters. The paper pays particular attention to the distinct methodologies applied at low (ℓ < 30) and high (ℓ > 30) multipole regions:

• Low-ℓ Likelihood: The analysis in the low-ℓ spectrum is predominantly concerned with the CMB's large scales, where cosmic variance is a significant consideration. This region provides critical insights into the Sachs-Wolfe plateau and the reionization bump.
• High-ℓ Likelihood: The high-ℓ region analysis involves more complex statistical treatment due to the vast amount of data available and the dominance of acoustic peaks. This part of the spectrum is essential for pinning down parameters such as the baryon density and the angular size of the sound horizon.

The paper also assesses the combined likelihoods from both the low and high-ℓ spectra to ensure consistency and improve overall parameter robustness.

Cosmological Implications

The Planck 2015 results have fortified the foundation of the ΛCDM model, also known as the standard model of cosmology. The precise measurements of the CMB power spectra have allowed for stringent constraints on parameters including the Hubble constant (H_0), the cosmic baryon density (Ω_bh^2), and the cold dark matter density (Ω_ch^2). These results display remarkable concordance with the theoretical expectations of inflationary cosmology.

Notably, the paper reinforces prior inferences concerning the total matter density (Ω_m) and the spectral index of primordial fluctuations (n_s), providing a deeper understanding of the inflationary dynamics in the early universe. Strong numerical results bolster the premise that the universe is spatially flat, albeit allowing slight deviations in curvature within the margin of observational error.

Robustness and Challenges

The robustness of the cosmological parameters derived from the Planck data is thoroughly tested against various systematic uncertainties and methodological choices. The paper lays out a critical analysis of potential biases, foreground emissions, and calibration errors that could influence the spectral measurements.

One of the challenges highlighted in the paper is the residual tension between certain parameter measures, such as the Hubble constant, when compared with independent astronomical observations. This incongruity has sparked further investigations and discussions within the cosmological community, possibly hinting at new physics or necessitating revisions in existing models.

Future Perspectives

The Planck 2015 analysis sets the stage for future research endeavors, especially in resolving the aforementioned tensions and in exploring beyond the ΛCDM model's framework. Prospective advances in observational cosmology might require integrating Planck data with forthcoming surveys from missions like the James Webb Space Telescope (JWST) and the Euclid satellite, which aim to provide complementary views of the universe's structure formation.

Consequently, this paper serves as a pivotal reference for ongoing and future investigations into the cosmos, ensuring that Planck's legacy continues to guide our quest for a comprehensive understanding of the universe's origins and evolution.