The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14 May 2009 and has been scanning the microwave and submillimetre sky continuously since 12 August 2009. In March 2013, ESA and the Planck Collaboration released the initial cosmology products based on the first 15.5 months of Planck data, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the mission and its performance, the processing, analysis, and characteristics of the data, the scientific results, and the science data products and papers in the release. The science products include maps of the cosmic microwave background (CMB) and diffuse extragalactic foregrounds, a catalogue of compact Galactic and extragalactic sources, and a list of sources detected through the Sunyaev-Zeldovich effect. The likelihood code used to assess cosmological models against the Planck data and a lensing likelihood are described. Scientific results include robust support for the standard six-parameter ΛCDM model of cosmology and improved measurements of its parameters, including a highly significant deviation from scale invariance of the primordial power spectrum. The Planck values for these parameters and others derived from them are significantly different from those previously determined. Several large-scale anomalies in the temperature distribution of the CMB, first detected by WMAP, are confirmed with higher confidence. Planck sets new limits on the number and mass of neutrinos, and has measured gravitational lensing of CMB anisotropies at greater than 25σ. Planck finds no evidence for non-Gaussianity in the CMB. Planck's results agree well with results from the measurements of baryon acoustic oscillations. Planck finds a lower Hubble constant than found in some more local measures. Some tension is also present between the amplitude of matter fluctuations (σ 8 ) derived from CMB data and that derived from Sunyaev-Zeldovich data. The Planck and WMAP power spectra are offset from each other by an average level of about 2% around the first acoustic peak. Analysis of Planck polarization data is not yet mature, therefore polarization results are not released, although the robust detection of E-mode polarization around CMB hot and cold spots is shown graphically.

We present a fully probabilistic, physical model of the non-linearly evolved density field, as probed by realistic galaxy surveys. Our model is valid in the linear and mildly non-linear regimes and uses second order Lagrangian perturbation theory to connect the initial conditions with the final density field. Our parameter space consists of the 3D initial density field and our method allows a fully Bayesian exploration of the sets of initial conditions that are consistent with the galaxy distribution sampling the final density field. A natural byproduct of this technique is an optimal non-linear reconstruction of the present density and velocity fields, including a full propagation of the observational uncertainties. A test of these methods on simulated data mimicking the survey mask, selection function and galaxy number of the SDSS DR7 main sample shows that this physical model gives accurate reconstructions of the underlying present-day density and velocity fields on scales larger than ∼ 6 Mpc/h. Our method naturally and accurately reconstructs non-linear features corresponding to three-point and higher order correlation functions such as walls and filaments. Simple tests of the reconstructed initial conditions show statistical consistency with the Gaussian simulation inputs. Our test demonstrates that statistical approaches based on physical models of the large scale structure distribution are now becoming feasible for realistic current and future surveys.

Conventional approaches to cosmology inference from galaxy redshift surveys are based on n-point functions, which are under rigorous perturbative control on sufficiently large scales. Here, we present an alternative approach, which employs a likelihood at the level of the galaxy density field. By integrating out small-scale modes based on effective-field theory arguments, we prove that this likelihood is under perturbative control if certain specific conditions are met. We further show that the information captured by this likelihood is equivalent to the combination of the next-to-leading order galaxy power spectrum, leadingorder bispectrum, and BAO reconstruction. Combined with MCMC sampling and MAP optimization techniques, our results allow for fully Bayesian cosmology inference from largescale structure that is under perturbative control. We illustrate this via a first demonstration of unbiased cosmology inference from nonlinear large-scale structure using this likelihood. In particular, we show unbiased estimates of the power spectrum normalization σ 8 from a catalog of simulated dark matter halos, where nonlinear information is crucial in breaking the b 1 − σ 8 degeneracy.

We describe an exact, flexible and computationally efficient algorithm for a joint inference of the large‐scale structure and its power spectrum, building on a Gibbs sampling framework and present its implementation ares (Algorithm for REconstruction and Sampling). ares is designed to reconstruct the 3D power spectrum together with the underlying dark matter density field in a Bayesian framework, under the reasonable assumption that the long‐wavelength Fourier components are Gaussian distributed. As a result ares does not only provide a single estimate but samples from the joint posterior of the power spectrum and density field conditional on a set of observations. This enables us to calculate any desired statistical summary, in particular we are able to provide joint uncertainty information. We apply our method to mock catalogues, with highly structured observational masks and selection functions, in order to demonstrate its ability to infer the power spectrum from real data sets, while fully accounting for any mask induced mode coupling.

In this work, we present the first non-linear, non-Gaussian full Bayesian large-scale structure analysis of the cosmic density field conducted so far. The density inference is based on the Sloan Digital Sky Survey (SDSS) Data Release 7, which covers the northern galactic cap. We employ a novel Bayesian sampling algorithm, which enables us to explore the extremely high dimensional non-Gaussian, non-linear lognormal Poissonian posterior of the three-dimensional density field conditional on the data. These techniques are efficiently implemented in the Hamiltonian Density Estimation and Sampling (HADES) computer algorithm and permit the precise recovery of poorly sampled objects and non-linear density fields. The nonlinear density inference is performed on a 750-Mpc cube with roughly 3-Mpc grid resolution, while accounting for systematic effects, introduced by survey geometry and selection function of the SDSS, and the correct treatment of a Poissonian shot noise contribution. Our highresolution results represent remarkably well the cosmic web structure of the cosmic density field. Filaments, voids and clusters are clearly visible. Further, we also conduct a dynamical web classification and estimate the web-type posterior distribution conditional on the SDSS data.