Cosmological weak lensing is the powerful probe of cosmology. Here we address one of the most fundamental, statistical questions inherent in weak lensing cosmology: whether or not we can recover the initial Gaussian information content of large-scale structure by combining the weak lensing observables, here focused on the weak lensing power spectrum and bispectrum. To address this question we fully take into account correlations between the power spectra of different multipoles and the bispectra of different triangle configurations, measured from a finite area survey. In particular we show that super-survey modes whose length scale is larger than or comparable with the survey size cause significant sample variance in the weak lensing correlations via the mode-coupling with sub-survey modes due to nonlinear gravitational clustering – the so-called super-sample variance. In this paper we discuss the origin of the super-sample variance and then study the information content inherent in the weak lensing correlation functions up to three-point level.

In the statistical framework of likelihood-free inference, the posterior distribution of model parameters is explored via simulation rather than direct evaluation of the likelihood function, permitting inference in situations where this function is analytically intractable. We consider the problem of estimating cosmological parameters using measurements of the weak gravitational lensing of galaxies; specifically, we propose the use a likelihood-free approach to investigate the posterior distribution of some parameters in the ΛCDM model upon observing a large number of sheared galaxies. The choice of summary statistic used when comparing observed data and simulated data in the likelihood-free inference framework is critical, so we work toward a principled method of choosing the summary statistic, aiming for dimension reduction while seeking a statistic that is as close as possible to being sufficient for the parameters of interest.

The weak lensing effect generates spin-2 distortions, referred to as shear, on the observable shape of distant galaxies, induced by intervening gravitational tidal fields. Traditionally, the spin-2 distortion in the light distribution of distant galaxies is measured in terms of a galaxy ellipticity. This is a very good unbiased estimator of the shear field in the limit that a galaxy is measured at infinite signal-to-noise. However, the ellipticity is always defined as a ratio between two quantities (for example, between the polarisation and measurement of the galaxy size, or between the semi-major and semi-minor axis of the galaxy) and therefore requires some non-linear combination of the image pixels. This means, in any realistic case, this would lead to biases in the measurement of the shear (and hence in the cosmological parameters) whenever noise is present in the image. This type of bias can be understood from the particular shape of the 2D probability distribution of the ellipticity of an object measured from data. Moreover this probability distribution can be used to explore strategies for calibration of noise biases in present and future weak lensing surveys (e.g. KiDS, DES, HSC,Euclid, LSST...)

Current and forthcoming cosmological data analyses share the challenge of huge datasets alongside increasingly tight requirements on the precision and accuracy of extracted cosmological parameters. The community is becoming increasingly aware that these requirements not only apply to the central values of parameters but, equally important, also to the error bars. Due to non-linear effects in the astrophysics, the instrument, and the analysis pipeline, data covariance matrices are usually not well known a priori and need to be estimated from the data itself, or from suites of large simulations. In either case, the finite number of realisations available to determine data covariances introduces significant biases and additional variance in the errors on cosmological parameters in a standard likelihood analysis. Here, we review recent work on quantifying these biases and additional variances and discuss approaches to remedy these effects.

Using the 3D information provided by photometric or spectroscopic weak lensing surveys, it has become possible in the last few years to address the problem of mapping the matter density contrast in three dimensions from gravitational lensing. We recently proposed a new non linear sparsity based reconstruction method allowing for high resolution reconstruction of the over-density. This new technique represents a significant improvement over previous linear methods and opens the way to new applications of 3D weak lensing density reconstruction. In particular, we demonstrate that for the first time reconstructed over-density maps can be used to detect and characterise galaxy clusters in mass and redshift.

Peak statistics from weak gravitational lensing have been shown to be a promising tool for cosmology. Here we propose a new approach to predict weak lensing peak counts. For an arbitrary cosmology, we draw dark matter halos from the halo mass function, and calculate the number of peaks from the projected halo mass distribution. This procedure is much faster than time-consuming N-body simulations. By comparing these “fast simulations” to N-body runs, we find that the peak abundance is in very good agreement. Furthermore, our model is able to discriminate cosmologies with different sets of parameters, using high signal-to-noise peaks (≳ 4). This encourages us to examine the optimal combinations of parameters to this approach in the future.

Similarly to gravitational lensing effects like cosmic shear, cosmological γ-ray emission too is to some extent a tracer of the distribution of dark matter (DM) in the Universe. Intervening DM structures source gravitational lensing distortions of distant galaxy images, and those same galaxies can emit γ rays, either because they host astrophysical sources, or directly by particle DM annihilations or decays occurring in the galactic halo. If such γ rays exhibit correlation with the cosmic shear signal, this will provide novel information on the composition of the extragalactic γ-ray background.

Comparisons between observed and predicted strong lensing properties of galaxy clusters have been used to claim either tension or consistency with ΛCDM cosmology. However, standard approaches to such tests are unable to quantify the preference for one cosmology over another. We advocate a Bayesian approach whereby the parameters defining the scaling relation between Einstein radii and cluster mass are treated as the observables. We demonstrate a method of estimating the likelihood for observing these parameters under the ΛCDM framework, using the X-ray selected z > 0.5 MACS clusters as a case in point and employing both N-body and hydrodynamic simulations of clusters. We account for cluster lens triaxiality within the modelling of the likelihood function. Cluster selection criteria is found to play as important a role as the uncertainty related to the description of star formation and feedback.

The general problem of the statistics of the primordial curvature perturbation field in cosmology is reviewed. The search for non-Gaussian signatures in cosmological perturbations, originated from inflation in the early Universe is discussed both from the theoretical point of view and in connection with constraints coming from recent observations and future prospects for observing/constraining them.

Anomalies drive scientific discovery – they are associated with the cutting edge of the research frontier, and thus typically exploit data in the low signal-to-noise regime. In astronomy, the prevalence of systematics –- both “known unknowns” and “unknown unknowns” – combined with increasingly large datasets, the widespread use of ad hoc estimators for anomaly detection, and the “look-elsewhere” effect, can lead to spurious false detections. In this informal note, I argue that anomaly detection leading to discoveries of new physics requires a combination of physical understanding, careful experimental design to avoid confirmation bias, and self-consistent statistical methods. These points are illustrated with several concrete examples from cosmology.

Studying the non-Gaussianity (NG) of the Cosmic Microwave Background (CMB) is an extremely powerful tool to investigate the properties of the very early Universe. The Planck nominal mission CMB maps yielded unprecedented constraints on primordial non-Gaussianity providing with the highest precision test of the standard model of inflation. Planck's high sensitivity also allowed to find evidence for the first time of the late-time non-Gaussianity arising from the Lensing-Integrated Sachs Wolfe (ISW) cross correlation. In this talk I will give details on the Planck data analysis and I will discuss the theoretical implications of the results.

The Gaussian Kinematic Formula (GKF, see Adler and Taylor (2007,2011)) is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for cosmological data collections. In this paper, we implement Minkowski functionals on multipoles and needlet components of CMB fields, thus allowing a better control of cosmic variance and extraction of information on both harmonic and real domains; we then exploit the GKF to provide their expected values on spherical maps, in the presence of arbitrary sky masks, and under nonGaussian circumstances.

The global shape, or topology, of the universe is not constrained by the equations of General Relativity, which only describe the local universe. As a consequence, the boundaries of space are not fixed and topologies different from the trivial infinite Euclidean space are possible. The cosmic microwave background (CMB) is the most efficient tool to study topology and test alternative models. Multi-connected topologies, such as the 3-torus, are of great interest because they are anisotropic and allow us to test a possible violation of isotropy in CMB data. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics encodes a topological signature. This signature can be used to distinguish an infinite space from a multi-connected space on sizes larger than the diameter of the last scattering surface (DLSS). With the help of the Kullback-Leibler divergence, we set the size of the edge of the biggest distinguishable torus with CMB temperature fluctuations and E-modes of polarization to 1.15 DLSS. CMB temperature fluctuations allow us to detect universes bigger than the observable universe, whereas E-modes are efficient to detect universes smaller than the observable universe.

We present new measurements of Cosmic Infrared Background (CIB) anisotropies using Planck. Combining HFI data with IRAS, the angular auto- and cross-frequency power spectrum is measured from 143 to 3000 GHz. After careful removal of the contaminants (cosmic microwave background anisotropies, Galactic dust and Sunyaev-Zeldovich emission), and a complete study of systematics, the CIB power spectrum is measured with unprecedented signal to noise ratio from angular multipoles ℓ ~ 150 to 2500. The interpretation based on the halo model is able to associate star-forming galaxies with dark matter halos and their subhalos, using a parametrized relation between the dust-processed infrared luminosity and (sub-)halo mass, and it allows to simultaneously fit all auto- and cross- power spectra very well. We find that the star formation history is well constrained up to redshifts around 2, and agrees with recent estimates of the obscured star-formation density using Spitzer and Herschel. However, at higher redshift, the accuracy of the star formation history measurement is strongly degraded by the uncertainty in the spectral energy distribution of CIB galaxies. We also find that the mean halo mass which is most efficient at hosting star formation is log(Meff/M⊙) = 12.6 and that CIB galaxies have warmer temperatures as redshift increases.

The statistical properties of the temperature anisotropies and polarization of the of cosmic microwave background (CMB) radiation offer a powerful probe of the physics of the early universe. In recent works a statistical procedure based upon the calculation of the kurtosis and skewness of the data in patches of CMB sky-sphere has been proposed and used to investigate the large-angle deviation from Gaussianity in WMAP maps. Here we briefly address the question as to how this analysis of Gaussianity is modified if the foreground-cleaned Planck maps are considered. We show that although the foreground-cleaned Planck maps present significant deviation from Gaussianity of different degrees when a less severe mask is used, they become consistent with Gaussianity, as detected by our indicators, when masked with the union mask U73.

We revisit recent claims of significant mirror-parity in CMB data from WMAP and Planck with a careful analysis using statistical estimators in both harmonic and pixel spaces. While the data indeed show significant signs of odd mirror-parity under some circumstances, the broad study shows that the results are not in significant tension with ΛCDM.

The Cold Spot is an anomalously cold region in the Cosmic Microwave Background (Vielva et al. 2004), either caused by a structure in the line of sight or could be of primordial origin. We search for a supervoid aligned with the Cold Spot region, filling the gap in redshift at z<0.3 which has never been explored in details. We find a large projected under density in the recently constructed WISE-2MASS catalogue, whose median redshift is z ≃ 0.14, with an angular size of 30 degrees. We show that a spherically symmetric Lemaitre-Tolman-Bondi (LTB) void model can simultaneously fit the δgal/b=δ2D≃ −0.12 underdensity in the WISE-2MASS catalogue, and the Cold Spot as observed by both the WMAP and Planck satellites. Such an LTB supervoid gives a plausible explanation of the Cold Spot anomaly, and is preferred over the null hypothesis or a texture model.

We present results from an end-to-end simulation pipeline of interferometric observations of cosmic microwave background polarization. We use both maximum-likelihood and Gibbs sampling techniques to estimate the power spectrum. In addition, we use Gibbs sampling for image reconstruction from interferometric visibilities. The results indicate the level to which various systematic errors (e.g., pointing errors, gain errors, beam shape errors, cross polarization) must be controlled in order to successfully detect and characterize primordial B modes and achieve other scientific goals. In addition, we show that Gibbs sampling is an effective method of image reconstruction for interferometric data in other astrophysical contexts.

The origin of large-scale magnetic fields is an unsolved problem in cosmology. In order to overcome, a possible scenario comes from the idea that these fields emerged from a small primordial magnetic field (PMF), produced in the early universe. This field could lead to the observed large-scales magnetic fields but also, would have left an imprint on the cosmic microwave background (CMB). In this work we summarize some statistical properties of this PMFs on the FLRW background. Then, we show the resulting PMF power spectrum using cosmological perturbation theory and some effects of PMFs on the CMB anisotropies.

In 2008, Granett et al. claimed a direct detection of the integrated Sachs- Wolfe (iSW) effect by a stacking approach of patches of the CMB, at the positions of identified superstructures. However, the high amplitude of their measured signal seems to be at odds with predictions from the standard model of cosmology. However, multiple questions arise from these results and their expected value : I propose here an original theoretical prediction of the iSW effect produced by such superstructures. I use simulations based on GR and the LTB metric to reproduce cosmic structures and predict their exact full theoretical iSW effect. Expected amplitudes are consistent with the measured signal ; however the latter shows non-reproducible features that are hardly compatible with ΛCDM predictions.