We study the flat-sky approximation for galaxy number counts including relativistic effects, and assess its performance and accuracy with respect to the full-sky result. We find an agreement of up to 5% for the local and lensing contributions to the 2-point correlation function and its multipoles at $z > 0.5$, and up to 1% for the multipoles alone at $z > 1$ and separations $\lesssim 250$ Mpc/$h$, with a speed-up of over a factor of 1000. Using a semi-analytic method, which has been implemented in a new version of the code COFFE, along with the Limber approximation for the integrated contributions, we further increase the performance, allowing the computation of the flat-sky multipoles to be done over 10000 times faster than in the full-sky calculation, which could be used to greatly speed-up Markov chain Monte Carlo sampling for cosmological parameter estimation.
We derive and test an approximation for the angular power spectrum of galaxy number counts in the flat sky limit. The standard density and redshift space distortion (RSD) terms in the resulting approximation are distinct to the Limber approximation, providing an accurate result for multipoles as low as $\ell\simeq10$, where the corresponding Limber approximation is completely inaccurate. At equal redshift the accuracy of the density and RSD (standard) terms is around 0.2% for $z<3$ and 0.5% at $z=5$, even to $\ell<50$. At unequal redshifts, if we consider the total power spectrum, the precisio…
We investigate the use of estimators of weak lensing power spectra based on a flat-sky implementation of the Pseudo-Cl (PCl) technique, where the masked shear field is transformed without regard for masked regions of sky. This masking mixes power, and E-convergence and B-modes. To study the accuracy of forward-modelling and full-sky power spectrum recovery we consider both large-area survey geometries, and small-scale masking due to stars and a checkerboard model for field-of-view gaps. The power spectrum for the large-area survey geometry is sparsely-sampled and highly oscillatory, which make…
We review the effect of the commonly-used Limber and flat-sky approximations on the calculation of shear power spectra and correlation functions for galaxy weak lensing. These approximations are accurate at small scales, but it has been claimed recently that their impact on low multipoles could lead to an increase in the amplitude of the mass fluctuations inferred from surveys such as CFHTLenS, reducing the tension between galaxy weak lensing and the amplitude determined by Planck from observations of the cosmic microwave background. Here, we explore the impact of these approximations on cosmo…
This article constructs flat-sky approximations in a controlled way in the context of the cosmic microwave background observations for the computation of both spectra and bispectra. For angular spectra, it is explicitly shown that there exists a whole family of flat-sky approximations of similar accuracy for which the expression and amplitude of next to leading order terms can be explicitly computed. It is noted that in this context two limiting cases can be encountered for which the expressions can be further simplified. They correspond to cases where either the sources are localized in a nar…
Cosmic Microwave Background lensing simulation by Taylor expansion has long been considered impractical due to slow convergence, but a recent flat-sky implementation shows that a simple trick eliminates this problem, making Taylor lensing a fast and simple lensing algorithm for the flat sky. Here we generalize the method to the full sky, and study its convergence and performance relative to a commonly used numerical code, Lenspix, with extensive benchmarks of both. Compared to the flat sky case, the method takes a speed hit due to the slow speed of spherical harmonic transforms compared to fas…
Mechanisms have been proposed that might rotate the linear polarization of the cosmic microwave background (CMB) as it propagates from the surface of last scatter. In the simplest scenario, the rotation will be uniform across the sky, but the rotation angle may also vary across the sky. We develop in detail the complete set of full-sky quadratic estimators for the rotation of the CMB polarization that can be constructed from the CMB temperature and polarization. We derive the variance with which these estimators can be measured and show that these variances reduce to the simpler flat-sky expre…
An important, and potentially detectable, signature of a non-trivial topology for the universe is the presence of so called circles-in-the-sky in the cosmic microwave background (CMB). Recent searches, confined to antipodal and nearly antipodal circles, have however failed to detect any. This outcome, coupled with recent theoretical results concerning the detectability of very nearly flat universes, is sufficient to exclude a detectable non-trivial cosmic topology for most observers in the inflationary limit ($0< |Ω_{tot}-1| \lesssim 10^{-5}$). In a recent paper we have studied the consequence…
To probe cosmological fields beyond the Gaussian level, three-point statistics can be used, all of which are related to the bispectrum. Hence, measurements of CMB anisotropies, galaxy clustering, and weak gravitational lensing alike have to rely upon an accurate theoretical background concerning the bispectrum and its noise properties. If only small portions of the sky are considered, it is often desirable to perform the analysis in the flat-sky limit. We aim at a formal, detailed derivation of the bispectrum covariance in the flat-sky approximation, focusing on a pure two-dimensional Fourier-…
Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at …
In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for the 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post- Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky w…
Efficient computation of the galaxy angular bispectrum in redshift space
Laboratoire d’Annecy de Physique Théorique, CNRS（阿讷西理论物理实验室，法国国家科学研究中心）；Institute of Astronomy（天文研究所）；Kavli Institute for Cosmology Cambridge（卡弗里宇宙学剑桥研究所）；Ruđer Bošković Institute（鲁德·博什科维奇研究所）；DAMTP, Centre for Mathematical Sciences（应用数学与理论物理系，数学科学中心）
Weak gravitational lensing of the 21 cm radiation is expected to be an important cosmological probe for post-reionization physics. We investigate the reconstruction of the matter density perturbations using a quadratic minimum variance estimator. The next generation of line intensity mapping (LIM) surveys such as HIRAX and CHIME will cover a larger sky fraction, which requires one to account for the curvature in the sky. Thus, we extend the plane-parallel flat-sky formalism for lensing reconstruction to account for a full-sky survey using the Spherical Fourier-Bessel (SFB) expansion. Using the…
Flat space models with multiply connected topology, which have compact dimensions, are tested against the distribution of high-redshift ($z \geq 4$) quasars of the Sloan Digital Sky Survey (SDSS). When the compact dimensions are smaller in size than the observed universe, topological lensing occurs, in which multiple images of single objects (ghost images) are observed. We improve on the recently introduced method to identify ghost images by means of four-point statistics. Our method is valid for any of the 17 multiply connected flat models, including nontoroial ones that are compactified by s…
We present wide-field near-infrared J and Ks images of the Andromeda Galaxy taken with WIRCam on the Canada-France-Hawaii Telescope (CFHT) as part of the Andromeda Optical and Infrared Disk Survey (ANDROIDS). This data set allows simultaneous observations of resolved stars and NIR surface brightness across M31's entire bulge and disk (within R=22 kpc). The primary concern of this work is the development of NIR observation and reduction methods to recover a uniform surface brightness map across the 3x1 degree disk of M31. This necessitates sky-target nodding across 27 WIRCam fields. Two sky-tar…
[Abridged] In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations - the so-called circles-in-the-sky. Searches for nearly antipodal circles in maps of cosmic microwave background have so far been unsuccessful. This negative outcome along with recent theoretical results concerning the detectability of nearly flat compact topologies is sufficient to exclude a detectable nontrivial topology for most observers in very nearly flat positively and negatively curved Universes ($0<…
By adopting the differential age method, we utilize selected 17832 luminous red galaxies (LRGs) from Sloan Digital Sky Survey Data Release Seven (SDSS DR7) covering redshift $0<z<0.4$ to measure Hubble parameters. Using a full spectrum fitting package UlySS, these spectra are reduced with single stellar population (SSP) models and optimal age information of our selected sample are derived. With the decreasing age-redshift relation, four new observational $H(z)$ data (OHD) points are obtained, which are $H(z)=69.0\pm19.6$ km s$^{-1}$ Mpc$^{-1}$ at $z=0.07$, $H(z)=68.6\pm26.2$ km s$^{-1}$ Mpc$^{…
We study the dipole anisotropy in number counts and flux density weighted number counts {or sky brightness} in the NRAO VLA Sky Survey (NVSS) data. The dipole anisotropy is expected due to our local motion with respect to the CMBR rest frame. We analyse data with an improved fit to the number density, n(S), as a function of the flux density S, which allows deviation from a pure power law behaviour. We also impose more stringent cuts to remove the contribution due to clustering dipole. In agreement with earlier results, we find that the amplitude of anisotropy is significantly larger in compari…
[Abridged] An observable signature of a detectable nontrivial spatial topology of the Universe is the circles-in-the-sky in the CMB sky. In the most general search, pairs of circles with deviation from antipodality $0^\circ \leq θ\leq 169^\circ$ and radii $10^\circ \leq λ\leq 90^\circ$ were investigated, but no matching circles were found. Assuming this negative result, we examine the question as to whether there are nearly flat universes with compact topology that would give rise to circles whose observable parameters $λ$ and $θ$ fall o outside the ranges covered by this search. We derive the…
We derive an exact expression for the correlation function in redshift shells including all the relativistic contributions. This expression, which does not rely on the distant-observer or flat-sky approximation, is valid at all scales and includes both local relativistic corrections and integrated contributions, like gravitational lensing. We present two methods to calculate this correlation function, one which makes use of the angular power spectrum C_ell(z1,z2) and a second method which evades the costly calculations of the angular power spectra. The correlation function is then used to defi…
We investigate the `Local Hole', an anomalous under-density in the local galaxy environment, by extending our previous galaxy $K-$band number-redshift and number-magnitude counts to $\approx 90\%$ of the sky. Our redshift samples are taken from the 2MASS Redshift Survey (2MRS) and the 2M++ catalogues, limited to $K<11.5$. We find that both surveys are in good agreement, showing an $\approx 21-22\%$ under-density at $z<0.075$ when compared to our homogeneous counts model that assumes the same luminosity function and other parameters as in our earlier papers. Using the Two Micron All Sky Survey …
Environmental statistics provide a necessary means of comparing the properties of galaxies in different environments and a vital test of models of galaxy formation within the prevailing, hierarchical cosmological model. We explore counts-in-cylinders, a common statistic defined as the number of companions of a particular galaxy found within a given projected radius and redshift interval. Galaxy distributions with the same two-point correlation functions do not necessarily have the same companion count distributions. We use this statistic to examine the environments of galaxies in the Sloan Dig…
We present a complete set of formulae for calculating the bispectra of CMB temperature and polarization anisotropies generated from non-Gaussianity in the vector and tensor mode perturbations. In the all-sky analysis it is found that the bispectrum formulae for the tensor and vector-mode non-Gaussianity formally take complicated forms compared to the scalar mode one because the photon transfer functions in the tensor and vector modes depend on the azimuthal angle between the direction of the wave number vector of the photon's perturbation and that of the line of sight. We demonstrate that flat…
We describe a 4.85 GHz survey of bright, flat-spectrum radio sources conducted with the Effelsberg 100 m telescope in an attempt to improve the completeness of existing surveys, such as CRATES. We report the results of these observations and of follow-up 8.4 GHz observations with the VLA of a subset of the sample. We comment on the connection to the WMAP point source catalog and on the survey's effectiveness at supplementing the CRATES sky coverage.
The Cosmological Principle states that the Universe is statistically isotropic and homogeneous on large scales. In particular, this implies statistical isotropy in the galaxy distribution, after removal of a dipole anisotropy due to the observer's motion. We test this hypothesis with number count maps from the NVSS radio catalogue. We use a local variance estimator based on patches of different angular radii across the sky and compare the source count variance between and within these patches. In order to assess the statistical significance of our results, we simulate radio maps with the NVSS …
