Related papers: Correspondence principle between spherical and Euc…
In a recent paper, Gurzadyan & Penrose claim to have found directions in the sky around which there are multiple concentric sets of annuli with anomalously low variance in the cosmic microwave background (CMB). These features are presented…
This paper studies random fields on the unit sphere. Traditionally, isotropic Gaussian random fields are considered as the underlying statistical model of the cosmic microwave background (CMB) data. This paper discusses the generalized…
Gravitational interaction of cosmic microwave background (CMB) photons with matter perturbations present along the line-of-sight to the surface of last scattering modifies the shape of the CMB anisotropy power spectrum. Here I focus on…
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…
The polarization of the Cosmic Microwave Background (CMB)is a powerful observational tool at hand for modern cosmology. It allows to break the degeneracy of fundamental cosmological parameters one cannot obtain using only anisotropy data…
This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its…
CMB (Cosmic Microwave Background) polarization observations test many aspects of cosmological models. Effective pseudoscalar-photon interaction(s) would induce a rotation of linear polarization of electromagnetic wave propagating with…
The current suite of results from Cosmic Microwave Background anisotropy experiments is fulfilling the promise of providing extraordinary levels of discrimination between cosmological models. We calculate a binned anisotropy power spectrum,…
Multiply connected space sections of the universe on a scale smaller than the horizon size can leave an imprint on cosmic microwave background polarization maps, in such a way that the so-called ``circles-in-the-sky'' method can be used to…
We discuss inhomogeneous cosmological models which satisfy the Copernican principle. We construct some inhomogeneous cosmological models starting from the ansatz that the all the observers in the models view an isotropic cosmic microwave…
For power spectrum estimation it's important that the pixelization of a CMB sky map be smooth and regular to high degree. With this criterion in mind the ``COBE sky cube" was defined. This paper has as central theme to further improve on…
In this article, we construct discrete tight frames for $L^2(\mathbb{S}^{d-1})$, $d\geq3$, which consist of localized polynomial wavelets with adjustable degrees of directionality. In contrast to the well studied isotropic case, these…
One of the main pillars of the {\Lambda}CDM model is the Cosmological Principle, which states that our Universe is statistically isotropic and homogeneous on large scales. Here we test this hypothesis using the Astrophysical Gravitational…
Cosmological inhomogeneities gravitationally deflect radiation propagating from distant sources, transforming the spatial and angular correlation functions of intrinsic source properties. For a gaussian distribution of deflections (e.g.…
Speckle metrology is a powerful tool in the measurement of wavelength and spectra. Recently, speckle produced by multiple reflections inside an integrating sphere has been proposed and showed high performance. However, to our knowledge, a…
Matter wave interferometry is becoming an increasingly important technique in quantum metrology. However, unlike its photonic counterpart, this technique relies on the interference of particles possessing a non-zero rest mass and an…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
The anisotropies in the cosmic microwave background (CMB) provide our best laboratory for testing models of the formation and evolution of large-scale structure. The rich features in the cosmic microwave background anisotropy spectrum, in…
The cosmic microwave background (CMB) is a significant source of knowledge about the origin and evolution of our universe. However, observations of the CMB are contaminated by foreground emissions, obscuring the CMB signal and reducing its…
Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the…