Related papers: The needlets bispectrum
We discuss a new scale-discretised directional wavelet transform to analyse spin signals defined on the sphere, in particular the polarisation of the cosmic microwave background (CMB).
Cosmological structures grow differently in theories of gravity which are modified as compared to Einstein's General relativity (GR). Cosmic microwave background (CMB) fluctuation patterns at the last scattering surface are lensed by these…
Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of…
We consider multifractal random wavelet series built from Gibbs measures, and study the singularity spectra associated with the graph and range of these functions restricted to their iso-H\"older sets. To obtain these singularity spectra,…
We study the position-dependent power spectrum and the integrated bispectrum statistic for 2D cosmological fields on the sphere (integrated angular bispectrum). First, we derive a useful, $m$-independent, formula for the full-sky integrated…
In this paper we develop the theory of clusterization of peaks in a Gaussian random field. We have obtained new mathematical results from this theory and the theory of percolation and have proposed a topological method of analysis of sky…
This second paper of two companion papers on the estimation of power spectra specializes to the topic of estimating galaxy power spectra at large, linear scales using maximum likelihood methods. As in the first paper, the aims are…
Curvelets are efficient to represent highly anisotropic signal content, such as a local linear and curvilinear structure. First-generation curvelets on the sphere, however, suffered from blocking artefacts. We present a new…
Modeling the nonlinearity of the halo bispectrum remains a major challenge in modern cosmology, in particular for ongoing and upcoming large-scale structure observations that are performed to study the inflationary physics. The "power…
This article presents the first computation of the complete bispectrum of the cosmic microwave background temperature anisotropies arising from the evolution of all cosmic fluids up to second order, including neutrinos. Gravitational…
Prior to photon decoupling magnetic random fields of comoving intensity in the nano-Gauss range distort the temperature and the polarization anisotropies of the microwave background, potentially induce a peculiar B-mode power spectrum and…
Homogeneity is a crucial, but poorly tested, assumption in cosmology. We introduce a new approach which allows us to place limits on the presence of localized structures within essentially our entire observable volume, using cosmic…
We propose a set of new statistics which can be extracted out of the angular distribution of the Fourier transform of the temperature anisotropies in the small field limit. They quantify generic non-Gaussian structure and complement the…
This paper focuses on two aspects of the statistics of cosmological observables that are important for the next stages of precision cosmology. First, we note that the theory of reduced angular $N$-point spectra has only been developed in…
We calculate the Cosmic Microwave Background anisotropy bispectrum on large angular scales in the absence of primordial non-Gaussianities, assuming exact matter dominance and extending at second order the classic Sachs-Wolfe result \delta…
Context. The overdensity inside a cosmological sub-volume and the tidal fields from its surroundings affect the matter distribution of the region. The resulting difference between the local and global power spectra is characterized by the…
Combination of the power spectrum and bispectrum is a powerful way of breaking degeneracies between galaxy bias and cosmological parameters, enabling us to maximize the constraining power from galaxy surveys. Recent cosmological constraints…
This article investigates the non-linear evolution of cosmological perturbations on sub-Hubble scales in order to evaluate the unavoidable deviations from Gaussianity that arise from the non-linear dynamics. It shows that the dominant…
Series expansions of isotropic Gaussian random fields on $\mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…