Context. High-precision cosmology requires the analysis of large-scale surveys in 3D spherical coordinates, i.e. spherical Fourier-Bessel decomposition. Current methods are insufficient for future ...data-sets from wide-field cosmology surveys. Aims. The aim of this paper is to present a public code for fast spherical Fourier-Bessel decomposition that can be applied to cosmological data or 3D data in spherical coordinates in other scientific fields. Methods. We present an equivalent formulation of the spherical Fourier-Bessel decomposition that separates radial and tangential calculations. We propose to use the existing pixelisation scheme HEALPix for a rapid calculation of the tangential modes. Results. 3DEX (3D EXpansions) is a public code for fast spherical Fourier-Bessel decomposition of 3D all-sky surveys that takes advantage of HEALPix for the calculation of tangential modes. We perform tests on very large simulations and we compare the precision and computation time of our method with an optimised implementation of the spherical Fourier-Bessel original formulation. For surveys with millions of galaxies, computation time is reduced by a factor 4–12 depending on the desired scales and accuracy. The formulation is also suitable for pre-calculations and external storage of the spherical harmonics, which allows for additional speed improvements. The 3DEX code can accommodate data with masked regions of missing data. 3DEX can also be used in other disciplines, where 3D data are to be analysed in spherical coordinates.
Weak gravitational lensing provides a sensitive probe of cosmology by measuring the mass distribution and the geometry of the low-redshift Universe. We show how an all-sky weak lensing tomographic ...survey can jointly constrain different sets of cosmological parameters describing dark energy, massive neutrinos (hot dark matter) and the primordial power spectrum. In order to put all sectors on an equal footing, we introduce a new parameter β, the second-order running spectral index. Using the Fisher matrix formalism with and without cosmic microwave background (CMB) priors, we examine how the constraints vary as the parameter set is enlarged. We find that weak lensing with CMB priors provides robust constraints on dark energy parameters and can simultaneously provide strong constraints on all three sectors. We find that the dark energy sector is largely insensitive to the inclusion of the other cosmological sectors. Implications for the planning of future surveys are discussed.
PyCosmo is a Python-based framework for the fast computation of cosmological model predictions. One of its core features is the symbolic representation of the Einstein–Boltzmann system of equations. ...Efficient C/C++ code is generated from the SymPy symbolic expressions making use of the sympy2c package. This enables easy extensions of the equation system for the implementation of new cosmological models. We illustrate this with three extensions of the PyCosmo Boltzmann solver to include a dark energy component with a constant equation of state, massive neutrinos and a radiation streaming approximation. We describe the PyCosmo framework, highlighting new features, and the symbolic implementation of the new models. We compare the PyCosmo predictions for the ΛCDM model extensions with CLASS, both in terms of accuracy and computational speed. We find a good agreement, to better than 0.1% when using high-precision settings and a comparable computational speed. Links to the Python Package Index (PyPI) page of the code release and to the PyCosmo Hub, an online platform where the package is installed, are available at: https://cosmology.ethz.ch/research/software-lab/PyCosmo.html.
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localized basis ...functions of different shapes, which we call ‘shapelets’. A particularly useful set of complete and orthonormal shapelets is that consisting of weighted Hermite polynomials, which correspond to perturbations around a circular Gaussian. They are also the eigenstates of the two dimensional quantum harmonic oscillator, and thus allow us to use the powerful formalism developed for this problem. One of their special properties is their invariance under Fourier transforms (up to a rescaling), leading to an analytic form for convolutions. The generator of linear transformations such as translations, rotations, shears and dilatations can be written as simple combinations of raising and lowering operators. We derive analytic expressions for practical quantities, such as the centroid (astrometry), flux (photometry) and radius of the object, in terms of its shapelet coefficients. We also construct polar basis functions which are eigenstates of the angular momentum operator, and thus have simple properties under rotations. As an example, we apply the method to Hubble Space Telescope images, and show that the small number of shapelet coefficients required to represent galaxy images lead to compression factors of about 40 to 90. We discuss applications of shapelets for the archival of large photometric surveys, for weak and strong gravitational lensing and for image deprojection.
With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever-greater precision. However, this increased accuracy also places greater demands on ...the statistical tools used to extract the available information. To date, the majority of lensing analyses use the two-point statistics of the cosmic shear field. These can be either studied directly using the two-point correlation function or in Fourier space, using the power spectrum. But analysing weak lensing data inevitably involves the masking out of regions, for example to remove bright stars from the field. Masking out the stars is common practice but the gaps in the data need proper handling. In this paper, we show how an inpainting technique allows us to properly fill in these gaps with only Nlog N operations, leading to a new image from which we can compute straightforwardly and with a very good accuracy both the power spectrum and the bispectrum. We then propose a new method to compute the bispectrum with a polar fft algorithm, which has the main advantage of avoiding any interpolation in the Fourier domain. Finally, we propose a new method for dark matter mass map reconstruction from shear observations, which integrates this new inpainting concept. A range of examples based on 3D N-body simulations illustrates the results.
This paper presents a new method for the reconstruction of weak lensing mass maps. It uses the multiscale entropy concept, which is based on wavelets, and the False Discovery Rate (FDR) which allows ...us to derive robust detection levels in wavelet space. We show that this new restoration approach outperforms several standard techniques currently used for weak shear mass reconstruction. This method can also be used to separate E and B modes in the shear field, and thus test for the presence of residual systematic effects. We concentrate on large blind cosmic shear surveys, and illustrate our results using simulated shear maps derived from N-Body ΛCDM simulations (Vale & White 2003) with added noise corresponding to both ground-based and space-based observations.
Cosmic shear requires high precision measurement of galaxy shapes in the presence of the observational point spread function (PSF) that smears out the image. The PSF must therefore be known for each ...galaxy to a high accuracy. However, for several reasons, the PSF is usually wavelength dependent; therefore, the differences between the spectral energy distribution of the observed objects introduce further complexity. In this paper, we investigate the effect of the wavelength dependence of the PSF, focusing on instruments in which the PSF size is dominated by the diffraction limit of the telescope and which use broad-band filters for shape measurement. We first calculate biases on cosmological parameter estimation from cosmic shear when the stellar PSF is used uncorrected. Using realistic galaxy and star spectral energy distributions and populations and a simple three-component circular PSF, we find that the colour dependence must be taken into account for the next generation of telescopes. We then consider two different methods for removing the effect: (i) the use of stars of the same colour as the galaxies and (ii) estimation of the galaxy spectral energy distribution using multiple colours and using a telescope model for the PSF. We find that both of these methods correct the effect to levels below the tolerances required for per cent level measurements of dark energy parameters. Comparison of the two methods favours the template-fitting method because its efficiency is less dependent on galaxy redshift than the broad-band colour method and takes full advantage of deeper photometry.
ABSTRACT
The next generation of weak lensing surveys will measure the matter distribution of the local universe with unprecedented precision, allowing the resolution of non-Gaussian features of the ...convergence field. This encourages the use of higher-order mass-map statistics for cosmological parameter inference. We extend the forward-modelling based methodology introduced in a previous forecast paper to match these new requirements. We provide multiple forecasts for the $w$CDM parameter constraints that can be expected from stage 3 and 4 weak lensing surveys. We consider different survey setups, summary statistics and mass map filters including wavelets. We take into account the shear bias, photometric redshift uncertainties, and intrinsic alignment. The impact of baryons is investigated and the necessary scale cuts are applied. We compare the angular power spectrum analysis to peak and minima counts as well as Minkowski functionals of the mass maps. We find a preference for Starlet over Gaussian filters. Our results suggest that using a survey setup with 10 instead of 5 tomographic redshift bins is beneficial. Adding cross-tomographic information improves the constraints on cosmology and especially on galaxy intrinsic alignment for all statistics. In terms of constraining power, we find the angular power spectrum and the peak counts to be equally matched for stage 4 surveys, followed by minima counts and the Minkowski functionals. Combining different summary statistics significantly improves the constraints and compensates the stringent scale cuts. We identify the most ‘cost-effective’ combination to be the angular power spectrum, peak counts and Minkowski functionals following Starlet filtering.
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