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The last years have been an exciting period for the field of the Cosmic Microwave Background (CMB) research. With recent CMB balloon-borne and ground-based experiments we are entering a new era of 'precision' cosmology that enables us to…

This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange…

The cosmological birefringence caused by the coupling between the cosmic scalar field and the cosmic microwave background (CMB) photons through the Chern-Simons term can rotate the polarization planes of the photons, and mix the CMB E-mode…

Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…

This is a very exciting time for the CMB field. It is widely recognized that precision measurements of the CMB can provide a definitive test of cosmological models and determine their parameters accurately. At present observations give us…

The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we…

In the near future, observations of the cosmic microwave background (CMB) anisotropies will provide accurate determinations of many fundamental cosmological parameters. In this paper, we analyse degeneracies among cosmological parameters to…

We predict the polarization of cosmic microwave background (CMB) photons that results from a cosmic bubble collision. The polarization is purely E-mode, symmetric around the axis pointing towards the collision bubble, and has several…

I develop a method for assessing the ability of an instrument, coupled with an observing strategy, to measure the angular power spectrum of the cosmic microwave background (CMB). It allows for efficient calculation of expected parameter…

I consider the case of anisotropies in the Cosmic Microwave Background (CMB) from one single ordered perturbation source, or seed, existing well before decoupling between matter and radiation. Such structures could have been left by high…

The deflection of ultra-high energy cosmic rays depends on the shape of the injection spectrum of the source and the pervasive cosmic magnetic fields. In this work it is applied the wavelet transform on the sphere to search for energy…

The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…

A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L…

Observations of the cosmic microwave background (CMB), especially of its frequency spectrum and its anisotropies, both in temperature and in polarization, have played a key role in the development of modern cosmology and our understanding…

We present new clean maps of the CMB temperature anisotropies (as measured by Planck) constructed with a novel internal linear combination (ILC) algorithm using directional, scale-discretised wavelets --- Scale-discretised, directional…

Most cosmic microwave background experiments observe the sky along circular or near-circular scans on the celestial sphere. For such experiments, we show that simple linear systems connect the Fourier spectra of temperature and polarization…

A conventional explanation of the dipole anisotropy of the cosmic microwave background (CMB) radiation is in terms of the Doppler effect: our galaxy is moving with respect to CMB frame with $ \sim 600 ~ km ~ s^{-1} $. However, as the deep…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the…

The frequency spectrum of the cosmic microwave background (CMB) is a relatively untapped source of data which can allow us to peer beyond the surface of last scattering. Small deviations away from a perfect blackbody shape will encode…