Related papers: Spherical bispectrum expansion and quadratic estim…
We propose optimal estimators for bispectra from excited states. Two common properties of such bispectra are the enhancement in the collinear limit, and the prediction of oscillating features. We review the physics behind excited states and…
We present a detailed implementation of two bispectrum estimation methods which can be applied to general non-separable primordial and CMB bispectra. The method exploits bispectrum mode decompositions on the domain of allowed wavenumber or…
Cosmic microwave background (CMB) lensing is an integrated effect whose kernel is greater than half the peak value in the range $1<z<5$. Measuring this effect offers a powerful tool to probe the large-scale structure of the Universe at high…
We compute the spherical-sky weak-lensing power spectrum of the shear and convergence. We discuss various approximations, such as flat-sky, and first- and second- order Limber equations for the projection. We find that the impact of…
We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. With broad, overlapping radial window functions, these…
We derive optimal estimators for the two-, three-, and four-point correlators of statistically isotropic scalar fields defined on the sphere, such as the Cosmic Microwave Background temperature fluctuations, allowing for arbitrary (linear)…
In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which…
Total-angular-momentum (TAM) waves provide a set of basis functions for scalar, vector, and tensor fields that can be used in place of plane waves and that reflect the rotational symmetry of the spherical sky. Here we discuss three-point…
Spherical confinement in 3D harmonic, quartic and other higher oscillators of even order is studied. The generalized pseudospectral method is employed for accurate solution of relevant Schr\"odinger equation in an \emph{optimum,…
We present a comprehensive full-sky 3-dimensional analysis of the weak-lensing fields and their corresponding power spectra. Using the formalism of spin-weight spherical harmonics and spherical Bessel functions, we relate the two-point…
The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on…
We investigate the connection between the full- and flat-sky angular power spectra. First, we revisit this connection established on the geometric and physical grounds, namely that the angular correlations on the sphere and in the plane…
Polarization data will soon provide the best avenue for measurements of the CMB lensing potential, although it is potentially sensitive to several instrumental effects including beam asymmetry, polarization angle uncertainties, sky…
The CMB bispectrum generated by second-order effects at recombination can be calculated analytically when one of the three modes has a wavelength much longer than the other two and is outside the horizon at recombination. This was pointed…
A rigorous method of calculating the electromagnetic field, the scattering matrix, and scattering cross-sections of an arbitrary finite three-dimensional optical system described by its permittivity distribution is presented. The method is…
We obtain new improved spectral projection estimates on manifolds of non-positive curvature, including sharp ones for relatively large spectral windows for general tori. Our results are stronger than those in an earlier work of the first…
This document supplements the release of the Planck 2018 CMB lensing pipeline, now made publicly available. It collects calculations relevant to curved-sky separable quadratic estimators in the spin-weight, position-space correlation…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
We obtain new optimal estimates for the $L^2(M)\to L^q(M)$, $q\in (2,q_c]$, $q_c=2(n+1)/(n-1)$, operator norms of spectral projection operators associated with spectral windows $[\lambda,\lambda+\delta(\lambda)]$, with…
The squeezed limit of the three-point function of cosmological perturbations is a powerful discriminant of different models of the early Universe. We present a conceptually simple and complete framework to relate any primordial bispectrum…