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We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their angular and radial properties can be controlled independently. They are particularly suited to analyzing cosmological observations such as the weak gravitational lensing of galaxies. Such observations have a unique 3D geometrical setting since they are natively made on the sky, have spin angular symmetries, and are extended in the radial direction by additional distance or redshift iniormation. Flaglets are constructed in the harmonic space defined by the Fourier-Laguerre transform, previously defined for scalar functions and extended here to signals with spin symmetries. Thanks to various sampling theorems, both the Fourier-Laguerre and flaglet transforms are theoretically exact when applied to bandlimited signals. In other words, in numerical computations the only loss of information is due to the finite representation of floating point numbers. We develop a 3D framework relating the weak lensing power spectrum to covariances of flaglet coefficients. We suggest that the resulting novel flaglet weak lensing estimator offers a powerful alternative to common 2D and 3D approaches to accurately capture cosmological information. While standard weak lensing analyses focus on either real- or harmonic-space representations (i.e., correlation functions or Fourier-Bessel power spectra, respectively), a wavelet approach inherits the advantages of both techniques, where both complicated sky coverage and uncertainties associated with the physical modeling of small scales can be handled effectively. Our codes to compute the Fourier-Laguerre and flaglet transforms are made publicly available. [ABSTRACT FROM AUTHOR]

A number of theoretically well-motivated additions to the standard cosmological model predict weak signatures in the form of spatially localized sources embedded in the cosmic microwave background (CMB) fluctuations. We present a hierarchical Bayesian statistical formalism and a complete data analysis pipeline for testing such scenarios. We derive an accurate approximation to the full posterior probability distribution over the parameters defining any theory that predicts sources embedded in the CMB, and perform an extensive set of tests in order to establish its validity. The approximation is implemented using a modular algorithm, designed to avoid a posteriori selection effects, which combines a candidatedetection stage with a full Bayesian model-selection and parameter-estimation analysis. We apply this pipeline to theories that predict cosmic textures and bubble collisions, extending previous analyses by using: (1) adaptive-resolution techniques, allowing us to probe features of arbitrary size, and (2) optimal filters, which provide the best possible sensitivity for detecting candidate signatures. We conclude that the WMAP 7-year data do not favor the addition of either cosmic textures or bubble collisions to ACDM, and place robust constraints on the predicted number of such sources. The expected numbers of bubble collisions and cosmic textures on the CMB sky within our detection thresholds are constrained to be fewer than 4.0 and 5.2 at 95% confidence, respectively. [ABSTRACT FROM AUTHOR]

We present a method to measure the growth of structure and the background geometry of the Universe--with no a priori assumption about the underlying cosmological model. Using Canada-France-Hawaii Lensing Survey (CFHTLenS) shear data, we simultaneously reconstruct the lensing amplitude, the linear intrinsic alignment amplitude, the redshift evolving matter power spectrum, P(k,z), and the comoving distance, r(z). We find that lensing predominately constrains a single global power spectrum amplitude and several comoving distance bins. Our approach can localize the precise scales (k-modes in the matter power spectrum) and redshifts where lambda-cold dark matter (LCDM) fails--if any. We find that below z=0.4, the measured comoving distance r(z) is higher than that expected from the Planck LCDM cosmology by ∼1.5σ, while at higher redshifts, our reconstruction is fully consistent. To validate our reconstruction, we compare LCDM parameter constraints from the standard cosmic shear likelihood analysis to those found by fitting to the nonparametric information and we find good agreement. [ABSTRACT FROM AUTHOR]

Upcoming photometric lensing surveys will considerably tighten constraints on the neutrino mass and the dark energy equation of state. Nevertheless it remains an open question of how to optimally extract the information and how well the matter power spectrum must be known to obtain unbiased cosmological parameter estimates. By performing a principal component analysis (PCA), we quantify the sensitivity of 3D cosmic shear and tomography with different binning strategies to different regions of the lensing kernel and matter power spectrum, and hence the background geometry and growth of structure in the Universe. We find that a large number of equally spaced tomographic bins in redshift can extract nearly all the cosmological information without the additional computational expense of 3D cosmic shear. Meanwhile a large fraction of the information comes from small poorly understood scales in the matter power spectrum, that can lead to biases on measurements of cosmological parameters. In light of this, we define and compute a cosmology-independent measure of the bias due to imperfect knowledge of the power spectrum. For a Euclid-like survey, we find that the power spectrum must be known to an accuracy of less than 1% on scales with k≤7h Mpc-1. This requirement is not absolute since the bias depends on the magnitude of modeling errors, where they occur in k-z space, and the correlation between them, all of which are specific to any particular model. We therefore compute the bias in several of the most likely modeling scenarios and introduce a general formalism and public code, RequiSim, to compute the expected bias from any nonlinear model. [ABSTRACT FROM AUTHOR]

We introduce the Generalised Lensing and Shear Spectra (GLaSS) code which is available for download from https://github.com/astro-informatics/GLaSS It is a fast and flexible public code, written in Python, that computes generalized spherical cosmic shear spectra. The commonly used tomographic and spherical Bessel lensing spectra come as built-in run-mode options. GLaSS is integrated into the Cosmosis modular cosmological pipeline package. We outline several computational choices that accelerate the computation of cosmic shear power spectra. Using GLaSS, we test whether the assumption that using the lensing and projection kernels for a spatially-flat universe--in a universe with a small amount of spatial curvature--negligibly impacts the lensing spectrum. We refer to this assumption as the spatially-flat universe approximation, that has been implicitly assumed in all cosmic shear studies to date. We confirm that the spatially-flat universe approximation has a negligible impact on Stage IV cosmic shear experiments. [ABSTRACT FROM AUTHOR]

Density-estimation likelihood-free inference (DELFI) has recently been proposed as an efficient method for simulation-based cosmological parameter inference. Compared to the standard likelihood-based Markov chain Monte Carlo (MCMC) approach, DELFI has several advantages: it is highly parallelizable, there is no need to assume a possibly incorrect functional form for the likelihood, and complicated effects (e.g., the mask and detector systematics) are easier to handle with forward models. In light of this, we present two DELFI pipelines to perform weak lensing parameter inference with log-normal realizations of the tomographic shear field--using the Cℓ summary statistic. The first pipeline accounts for the non-Gaussianities of the shear field, intrinsic alignments, and photometric-redshift error. We validate that it is accurate enough for Stage III experiments and estimate that O(1000) simulations are needed to perform inference on Stage IV data. By comparing the second DELFI pipeline, which makes no assumption about the functional form of the likelihood, with the standard MCMC approach, which assumes a Gaussian likelihood, we test the impact of the Gaussian likelihood approximation in the MCMC analysis. We find it has a negligible impact on Stage IV parameter constraints. Our pipeline is a step towards seamlessly propagating all data-processing, instrumental, theoretical, and astrophysical systematics through to the final parameter constraints. [ABSTRACT FROM AUTHOR]