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Abstract. We compute the Bayesian evidence and complexity of 193 slow-roll single-field models of inflation using the Planck 2013 Cosmic Microwave Background data, with the aim of establishing which models are favoured from a Bayesian perspective. Our calculations employ a new numerical pipeline interfacing an inflationary effective likelihood with the slowroll library ASPIC and the nested sampling algorithm MultiNest. The models considered represent a complete and systematic scan of the entire landscape of inflationary scenarios proposed so far. Our analysis singles out the most probable models (from an Occam's razor point of view) that are compatible with Planck data, while ruling out with very strong evidence 34% of the models considered. We identify 26% of the models that are favoured by the Bayesian evidence, corresponding to 15 different potential shapes. If the Bayesian complexity is included in the analysis, only 9% of the models are preferred, corresponding to only 9 different potential shapes. These shapes are all of the plateau type.

The current flow of high accuracy astrophysical data, among which are the Cosmic Microwave Background (CMB) measurements by the Planck satellite, offers an unprecedented opportunity to constrain the inflationary theory. This is however a challenging project given the size of the inflationary landscape which contains hundreds of different scenarios. Given that there is currently no observational evidence for primordial non-Gaussianities, isocurvature perturbations or any other non-minimal extension of the inflationary paradigm, a reasonable approach is to consider the simplest models first, namely the slow-roll single field models with minimal kinetic terms. This still leaves us with a very populated landscape, the exploration of which requires new and efficient strategies. It has been customary to tackle this problem by means of approximate model independent methods while a more ambitious alternative is to study the inflationary scenarios one by one. We have developed the new publicly available runtime library ASPIC 1 to implement this last approach. The ASPIC code provides all routines needed to quickly derive reheating consistent observable predictions within this class of scenarios. ASPIC has been designed as an evolutive code which presently supports 74 different models, a number that may be compared with three or four representing the present state of the art. In this paper, for each of the ASPIC models, we present and collect new results in a systematic manner, thereby constituting the first Encyclopaedia Inflationaris. Finally, we discuss how this procedure and ASPIC could be used to determine the best model of inflation by means of Bayesian inference.

The existence of a scaling evolution for cosmic string loops in an expanding universe is demonstrated for the first time by means of numerical simulations. In contrast with what is usually assumed, this result does not rely on any gravitational back reaction effect and has been observed for loops as small as a few thousandths the size of the horizon. We give the energy and number densities of expected cosmic string loops in both the radiation and matter eras. Moreover, we quantify previous claims on the influence of the network initial conditions and the formation of numerically unresolved loops by showing that they only concern a transient relaxation regime. Some cosmological consequences are discussed.

We present the first Bayesian constraints on the single field inflationary reheating era obtained from Cosmic Microwave Background (CMB) data. After demonstrating that this epoch can be fully characterized by the so-called reheating parameter, we show that it is constrained by the seven years Wilkinson Microwave Anisotropies Probe (WMAP7) data for all large and small field models. An interesting feature of our approach is that it yields lower bounds on the reheating temperature which can be combined with the upper bounds associated with gravitinos production. For large field models, we find the energy scale of reheating to be higher than those probed at the Large Hadron Collider, ρ reh > 390 GeV forw reh = −0.2. The physical origin of these constraints is pedagogically explained by means of the slow-roll approximation. Finally, when marginalizing over all possible reheating history, the WMAP7 data push massive inflation under pressure (p < 2.2 at 95% of confidence where p is the power index of the large field potentials) while they slightly favor super-Planckian field expectation values in the small field models.

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.

Abstract.The implications of the WMAP (Wilkinson Microwave Anisotropy Probe) third year data for inflation are investigated using both the slow-roll approximation and an exact numerical integration of the inflationary power spectra including a phenomenological modelling of the reheating era. At slow-roll leading order, the constraints ǫ 1 < 0.022 and −0.07 < ǫ 2 < 0.07 are obtained at 95% CL (Confidence Level) implying a tensor-to-scalar ratio r 10 < 0.21 and a Hubble parameter during inflation H/m Pl < 1.3 × 10 −5 . At next-to-leading order, a tendency for ǫ 3 > 0 is observed. With regards to the exact numerical integration, large field models, V (φ) ∝ φ p , with p > 3.1 are now excluded at 95% CL. Small field models, V (φ) ∝ 1 − (φ/µ) p , are still compatible with the data for all values of p. However, if µ/m Pl < 10 is assumed, then the case p = 2 is slightly disfavoured. In addition, mild constraints on the reheating temperature for an extreme equation of state w reh −1/3 are found, namely T reh > 2 TeV at 95% CL. Hybrid models are disfavoured by the data, the best fit model having ∆χ 2 ≃ +5 with two extra parameters in comparison with large field models. Running mass models remain compatible, but no prior independent constraints can be obtained. Finally, superimposed oscillations of trans-Planckian origin are studied. The vanilla slow-roll model is still the most probable one. However, the overall statistical weight in favour of superimposed oscillations has increased in comparison with the WMAP first year data, the amplitude of the oscillations satisfying 2|x|σ 0 < 0.76 at 95% CL. The best fit model leads to an improvement of ∆χ 2 ≃ −12 for 3 extra parameters. Moreover, compared to other oscillatory patterns, the logarithmic shape is favoured.

This paper presents the Planck 2013 likelihood, a complete statistical description of the two-point 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, , covering 2 ≤ ≤ 2500. The main source of uncertainty at < ∼ 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher s. For < 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 ≥ 50, we employ a correlated Gaussian likelihood approximation based on a fine-grained set of angular cross-spectra 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 high-cross-spectra with residuals below a few µK 2 at < ∼ 1000, in agreement with estimated calibration uncertainties. We compare our results with foreground-cleaned CMB maps derived from all Planck frequencies, as well as with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. We further show that the best-fit ΛCDM cosmology is in excellent agreement with preliminary Planck EE and T E polarisation spectra. We find that the standard ΛCDM cosmology is well constrained by Planck from the measurements at < ∼ 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 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 best-fit ΛCDM model and the low-spectrum in the form of a power deficit of 5-10% at < ∼ 40, with a statistical significance of 2.5-3σ. 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.