Planck 2015 results. XIII. Cosmological parameters (1502.01589v3)

Abstract: We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

• The paper refines key cosmological parameters by integrating comprehensive temperature and polarization data from the Planck satellite.
• It employs robust statistical methods and cross-validation with external datasets to constrain measurements like the Hubble constant, matter density, and spectral index.
• The study supports the ΛCDM model and lays a foundation for future research on dark energy, dark matter, and inflationary conditions in the early Universe.

Analysis of Cosmological Parameters from Planck Data

The paper authored by the Planck Collaboration focuses on the detailed analysis of cosmological parameters using data acquired by the Planck satellite. The paper represents a significant contribution to the field of cosmology through its comprehensive analysis of the Cosmic Microwave Background (CMB) radiation. This work effectively utilizes the full set of Planck data, incorporating temperature and polarization information to derive constraints on several key cosmological parameters.

Methodology and Data Analysis

The analysis employs a robust methodological framework that integrates a variety of statistical tools and models to extract cosmological parameters from the CMB data, such as the Lambda Cold Dark Matter (ΛCDM) model. The paper not only uses the raw data collected by the Planck satellite but also cross-validates it with external datasets to refine the parameter estimates. Key datasets include the Planck-only temperature and polarization data, and third-party astrophysical observations which provide additional anchoring for the retrieval of these parameters.

Key Findings

The results obtained present a coherent picture of the Universe's composition and evolution, aligning closely with previous observations but with added precision. Notable numerical results include refined measurements of the Hubble constant, the matter density parameter, and the spectral index of primordial fluctuations. Of particular interest is the determination of the Hubble constant which remains a point of contention when compared with lower direct measurements from other observational methods.

Implications and Theoretical Insights

The refined cosmological parameters derived from the Planck data offer robust support for the ΛCDM model, substantiating theoretical predictions about the Universe's large-scale structure. The implications of these findings extend to understanding dark energy, dark matter, and the overall curvature of the Universe. This analysis also assists in constraining properties of inflationary models, an area of significant theoretical interest, by providing insights into the initial conditions of the Universe.

Future Directions

The paper lays the groundwork for future research in cosmology, particularly in the areas of inflationary theory and the pursuit of a more integrated model to explain dark energy and dark matter disparities. It is expected that subsequent observational missions, potentially incorporating more sensitive instrumentation, will leverage these findings to explore deeper into cosmic history and further refine cosmological models.

In conclusion, this paper stands as a substantial analytical achievement in extracting and refining cosmological parameters from CMB data. The data from Planck provides a benchmark for current and future cosmological studies, contributing to our understanding of the fundamental characteristics and evolution of the Universe.