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Understanding the nature of dark matter in the Universe is an important goal of modern cosmology. A key method for probing this distribution is via weak gravitational lensing mass-mapping - a challenging ill-posed inverse problem where one infers the convergence field from observed shear measurements. Upcoming stage IV surveys, such as those made by the Vera C. Rubin Observatory and Euclid satellite, will provide a greater quantity and precision of data for lensing analyses, necessitating high-fidelity mass-mapping methods that are computationally efficient and that also provide uncertainties for integration into downstream cosmological analyses. In this work we introduce MMGAN, a novel mass-mapping method based on a regularised conditional generative adversarial network (GAN) framework, which generates approximate posterior samples of the convergence field given shear data. We adopt Wasserstein GANs to improve training stability and apply regularisation techniques to overcome mode collapse, issues that otherwise are particularly acute for conditional GANs. We train and validate our model on a mock COSMOS-style dataset before applying it to true COSMOS survey data. Our approach significantly outperforms the Kaiser-Squires technique and achieves similar reconstruction fidelity as alternative state-of-the-art deep learning approaches. Notably, while alternative approaches for generating samples from a learned posterior are slow (e.g. requiring $\sim$10 GPU minutes per posterior sample), MMGAN can produce a high-quality convergence sample in less than a second.

We demonstrate the successful use of scattering representations without further compression for simulation-based inference (SBI) with images (i.e. field-level), illustrated with a cosmological case study. Scattering representations provide a highly effective representational space for subsequent learning tasks, although the higher dimensional compressed space introduces challenges. We overcome these through spatial averaging, coupled with more expressive density estimators. Compared to alternative methods, such an approach does not require additional simulations for either training or computing derivatives, is interpretable, and resilient to covariate shift. As expected, we show that a scattering only approach extracts more information than traditional second order summary statistics., Comment: 9 pages, 2 figures, accepted by NeurIPS workshop on Machine Learning and the Physical Sciences

Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build generative models of complex non-linear fields from a limited amount of data. In the context of upcoming cosmological surveys, the extension of these tools to spherical data is necessary. We develop scattering transforms on the sphere and focus on the construction of maximum-entropy generative models of astrophysical fields. The quality of the generative models, both statistically and visually, is very satisfying, which therefore open up a wide range of new applications for future cosmological studies., Comment: Contribution to the 2024 Cosmology session of the 58th Rencontres de Moriond. For details, please refer to the full article arXiv:2407.07007

Understanding the large-scale structure of the Universe and unravelling the mysteries of dark matter are fundamental challenges in contemporary cosmology. Reconstruction of the cosmological matter distribution from lensing observables, referred to as 'mass-mapping' is an important aspect of this quest. Mass-mapping is an ill-posed problem, meaning there is inherent uncertainty in any convergence map reconstruction. The demand for fast and efficient reconstruction techniques is rising as we prepare for upcoming surveys. We present a novel approach which utilises deep learning, in particular a conditional Generative Adversarial Network (cGAN), to approximate samples from a Bayesian posterior distribution, meaning they can be interpreted in a statistically robust manner. By combining data-driven priors with recent regularisation techniques, we introduce an approach that facilitates the swift generation of high-fidelity, mass maps. Furthermore, to validate the effectiveness of our approach, we train the model on mock COSMOS-style data, generated using Colombia Lensing's kappaTNG mock weak lensing suite. These preliminary results showcase compelling convergence map reconstructions and ongoing refinement efforts are underway to enhance the robustness of our method further., Comment: 2 pages, 1 figure, submitted for conference proceedings for '58th Recontres de Moriond', 2024

We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we combine (i) emulation, where a machine learning model is trained to mimic cosmological observables, e.g. CosmoPower-JAX; (ii) differentiable and probabilistic programming, e.g. JAX and NumPyro, respectively; (iii) scalable Markov chain Monte Carlo (MCMC) sampling techniques that exploit gradients, e.g. Hamiltonian Monte Carlo; and (iv) decoupled and scalable Bayesian model selection techniques that compute the Bayesian evidence purely from posterior samples, e.g. the learned harmonic mean implemented in harmonic. This paradigm allows us to carry out a complete Bayesian analysis, including both parameter estimation and model selection, in a fraction of the time of traditional approaches. First, we demonstrate the application of this paradigm on a simulated cosmic shear analysis for a Stage IV survey in 37- and 39-dimensional parameter spaces, comparing $\Lambda$CDM and a dynamical dark energy model ($w_0w_a$CDM). We recover posterior contours and evidence estimates that are in excellent agreement with those computed by the traditional nested sampling approach while reducing the computational cost from 8 months on 48 CPU cores to 2 days on 12 GPUs. Second, we consider a joint analysis between three simulated next-generation surveys, each performing a 3x2pt analysis, resulting in 157- and 159-dimensional parameter spaces. Standard nested sampling techniques are simply unlikely to be feasible in this high-dimensional setting, requiring a projected 12 years of compute time on 48 CPU cores; on the other hand, the proposed approach only requires 8 days of compute time on 24 GPUs. All packages used in our analyses are publicly available., Comment: 14 pages, 6 figures. Accepted for publication in the Open Journal of Astrophysics. Codes available at https://github.com/alessiospuriomancini/cosmopower, https://github.com/dpiras/cosmopower-jax, https://github.com/astro-informatics/harmonic/

We present the learned harmonic mean estimator with normalizing flows - a robust, scalable and flexible estimator of the Bayesian evidence for model comparison. Since the estimator is agnostic to sampling strategy and simply requires posterior samples, it can be applied to compute the evidence using any Markov chain Monte Carlo (MCMC) sampling technique, including saved down MCMC chains, or any variational inference approach. The learned harmonic mean estimator was recently introduced, where machine learning techniques were developed to learn a suitable internal importance sampling target distribution to solve the issue of exploding variance of the original harmonic mean estimator. In this article we present the use of normalizing flows as the internal machine learning technique within the learned harmonic mean estimator. Normalizing flows can be elegantly coupled with the learned harmonic mean to provide an approach that is more robust, flexible and scalable than the machine learning models considered previously. We perform a series of numerical experiments, applying our method to benchmark problems and to a cosmological example in up to 21 dimensions. We find the learned harmonic mean estimator is in agreement with ground truth values and nested sampling estimates. The open-source harmonic Python package implementing the learned harmonic mean, now with normalizing flows included, is publicly available., Comment: 14 pages, 8 figures, harmonic code available at https://github.com/astro-informatics/harmonic

The 21-cm hyperfine line of neutral hydrogen is a useful tool to probe the conditions of the Universe during the Dark Ages, Cosmic Dawn, and the Epoch of Reionisation. In most of the current calculations, the 21-cm line signals at given frequencies are computed, using an integrated line-of-sight line opacity, with the correction for cosmological expansion. These calculations have not fully captured the line and continuum interactions in the radiative transfer, in response to evolution of the radiation field and the variations of thermal and dynamic properties of the line-of-sight medium. We construct a covariant formulation for the radiative transfer of the 21-cm line and derive the cosmological 21-cm line radiative transfer (C21LRT) equation. The formulation properly accounts for local emission and absorption processes and the interaction between the line and continuum when the radiation propagates across the expanding Universe to the present observer. Our C21LRT calculations show that methods simply summing the line optical depth could lead to error of $5\%$ in the 21-cm signals for redshift $z \sim 12-35$ and of $>10\%$ for redshift $z \lesssim 8$. Proper covariant radiative transfer is therefore necessary for producing correct theoretical templates for extracting information of the structural evolution of the Universe through the Epoch of Reionisation from the 21-cm tomographic data., Comment: 16 pages, 11 figures, 3 tables

Cosmic strings are linear topological defects that may have been produced during symmetry-breaking phase transitions in the very early Universe. In an expanding Universe the existence of causally separate regions prevents such symmetries from being broken uniformly, with a network of cosmic string inevitably forming as a result. To faithfully generate observables of such processes requires computationally expensive numerical simulations, which prohibits many types of analyses. We propose a technique to instead rapidly emulate observables, thus circumventing simulation. Emulation is a form of generative modelling, often built upon a machine learning backbone. End-to-end emulation often fails due to high dimensionality and insufficient training data. Consequently, it is common to instead emulate a latent representation from which observables may readily be synthesised. Wavelet phase harmonics are an excellent latent representations for cosmological fields, both as a summary statistic and for emulation, since they do not require training and are highly sensitive to non-Gaussian information. Leveraging wavelet phase harmonics as a latent representation, we develop techniques to emulate string induced CMB anisotropies over a 7.2 degree field of view, with sub-arcminute resolution, in under a minute on a single GPU. Beyond generating high fidelity emulations, we provide a technique to ensure these observables are distributed correctly, providing a more representative ensemble of samples. The statistics of our emulations are commensurate with those calculated on comprehensive Nambu-Goto simulations. Our findings indicate these fast emulation approaches may be suitable for wide use in, e.g., simulation based inference pipelines. We make our code available to the community so that researchers may rapidly emulate cosmic string induced CMB anisotropies for their own analysis., Comment: code available at https://github.com/astro-informatics/stringgen

Uncertainty quantification is a crucial step of cosmological mass-mapping that is often ignored. Suggested methods are typically only approximate or make strong assumptions of Gaussianity of the shear field. Probabilistic sampling methods, such as Markov chain Monte Carlo (MCMC), draw samples form a probability distribution, allowing for full and flexible uncertainty quantification, however these methods are notoriously slow and struggle in the high-dimensional parameter spaces of imaging problems. In this work we use, for the first time, a trans-dimensional MCMC sampler for mass-mapping, promoting sparsity in a wavelet basis. This sampler gradually grows the parameter space as required by the data, exploiting the extremely sparse nature of mass maps in wavelet space. The wavelet coefficients are arranged in a tree-like structure, which adds finer scale detail as the parameter space grows. We demonstrate the trans-dimensional sampler on galaxy cluster-scale images where the planar modelling approximation is valid. In high-resolution experiments, this method produces naturally parsimonious solutions, requiring less than 1% of the potential maximum number of wavelet coefficients and still producing a good fit to the observed data. In the presence of noisy data, trans-dimensional MCMC produces a better reconstruction of mass-maps than the standard smoothed Kaiser-Squires method, with the addition that uncertainties are fully quantified. This opens up the possibility for new mass maps and inferences about the nature of dark matter using the new high-resolution data from upcoming weak lensing surveys such as Euclid.

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will discover an unprecedented number of supernovae (SNe), making spectroscopic classification for all the events infeasible. LSST will thus rely on photometric classification, whose accuracy depends on the not-yet-finalized LSST observing strategy. In this work, we analyze the impact of cadence choices on classification performance using simulated multi-band light curves. First, we simulate SNe with an LSST baseline cadence, a non-rolling cadence, and a presto-color cadence which observes each sky location three times per night instead of twice. Each simulated dataset includes a spectroscopically-confirmed training set, which we augment to be representative of the test set as part of the classification pipeline. Then, we use the photometric transient classification library snmachine to build classifiers. We find that the active region of the rolling cadence used in the baseline observing strategy yields a 25% improvement in classification performance relative to the background region. This improvement in performance in the actively-rolling region is also associated with an increase of up to a factor of 2.7 in the number of cosmologically-useful Type Ia supernovae relative to the background region. However, adding a third visit per night as implemented in presto-color degrades classification performance due to more irregularly sampled light curves. Overall, our results establish desiderata on the observing cadence related to classification of full SNe light curves, which in turn impacts photometric SNe cosmology with LSST., Comment: 22 pages, 14 figures. Changed to match version accepted by the Astrophysical Journal Supplement Series (accepted 06/02/2023)

We introduce two kurt-spectra to probe fourth-order statistics of weak lensing convergence maps. Using state-of-the-art numerical simulations, we study the shapes of these kurt-spectra as a function of source redshifts and smoothing angular scales. We employ a pseudo-$C_{\ell}$ approach to estimate the spectra from realistic convergence maps in the presence of an observational mask and noise for stage-IV large-scale structure surveys. We compare these results against theoretical predictions calculated using the FFTLog formalism, and find that a simple nonlinear clustering model-the hierarchical ansatz-can reproduce the numerical trends for the kurt-spectra in the nonlinear regime. In addition, we provide estimators for beyond fourth-order spectra where no definitive analytical results are available, and present corresponding results from numerical simulations., Comment: 32 pages, 6 figures, accepted for publication in JCAP

The Vera C. Rubin Observatory will increase the number of observed supernovae (SNe) by an order of magnitude; however, it is impossible to spectroscopically confirm the class for all the SNe discovered. Thus, photometric classification is crucial but its accuracy depends on the not-yet-finalized observing strategy of Rubin Observatory's Legacy Survey of Space and Time (LSST). We quantitatively analyze the impact of the LSST observing strategy on SNe classification using simulated multi-band light curves from the Photometric LSST Astronomical Time-Series Classification Challenge (PLAsTiCC). First, we augment the simulated training set to be representative of the photometric redshift distribution per supernovae class, the cadence of observations, and the flux uncertainty distribution of the test set. Then we build a classifier using the photometric transient classification library snmachine, based on wavelet features obtained from Gaussian process fits, yielding similar performance to the winning PLAsTiCC entry. We study the classification performance for SNe with different properties within a single simulated observing strategy. We find that season length is important, with light curves of 150 days yielding the highest performance. Cadence also has an important impact on SNe classification; events with median inter-night gap <3.5 days yield higher classification performance. Interestingly, we find that large gaps (>10 days) in light curve observations do not impact performance if sufficient observations are available on either side, due to the effectiveness of the Gaussian process interpolation. This analysis is the first exploration of the impact of observing strategy on photometric supernova classification with LSST., Comment: 18 pages, 13 figures. Changed to match version accepted by the Astrophysical Journal Supplement Series (accepted 28/10/2021). Software publicly available at https://github.com/LSSTDESC/snmachine

To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the $\textit{flat-sky approximation}$ has been sufficiently satisfied. However, with Stage IV surveys ($\textit{e.g. LSST}$ and $\textit{Euclid}$) imminent, extending mass-mapping techniques to the sphere is a fundamental necessity. As such, we extend the sparse hierarchical Bayesian mass-mapping formalism presented in previous work to the spherical sky. For the first time, this allows us to construct $\textit{maximum a posteriori}$ spherical weak lensing dark-matter mass-maps, with principled Bayesian uncertainties, without imposing or assuming Gaussianty. We solve the spherical mass-mapping inverse problem in the analysis setting adopting a sparsity promoting Laplace-type wavelet prior, though this theoretical framework supports all log-concave posteriors. Our spherical mass-mapping formalism facilitates principled statistical interpretation of reconstructions. We apply our framework to convergence reconstruction on high resolution N-body simulations with pseudo-Euclid masking, polluted with a variety of realistic noise levels, and show a significant increase in reconstruction fidelity compared to standard approaches. Furthermore we perform the largest joint reconstruction to date of the majority of publicly available shear observational datasets (combining DESY1, KiDS450 and CFHTLens) and find that our formalism recovers a convergence map with significantly enhanced small-scale detail. Within our Bayesian framework we validate, in a statistically rigorous manner, the community's intuition regarding the need to smooth spherical Kaiser-Squires estimates to provide physically meaningful convergence maps. Such approaches cannot reveal the small-scale physical structures that we recover within our framework.

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 lognormal realizations of the tomographic shear field -- using the C_l 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., Comment: Physical Review D. accepted

Polarization of radiation is a powerful tool to study cosmic magnetism and analysis of polarization can be used as a diagnostic tool for large-scale structures. In this paper, we present a solid theoretical foundation for using polarized light to investigate large-scale magnetic field structures: the cosmological polarized radiative transfer (CPRT) formulation. The CPRT formulation is fully covariant. It accounts for cosmological and relativistic effects in a self-consistent manner and explicitly treats Faraday rotation, as well as Faraday conversion, emission, and absorption processes. The formulation is derived from the first principles of conservation of phase-space volume and photon number. Without loss of generality, we consider a flat Friedmann-Robertson-Walker (FRW) space-time metric and construct the corresponding polarized radiative transfer equations. We propose an all-sky CPRT calculation algorithm, based on a ray-tracing method, which allows cosmological simulation results to be incorporated and, thereby, model templates of polarization maps to be constructed. Such maps will be crucial in our interpretation of polarized data, such as those to be collected by the Square Kilometer Array (SKA). We describe several tests which are used for verifying the code and demonstrate applications in the study of the polarization signatures in different distributions of electron number density and magnetic fields. We present a pencil-beam CPRT calculation and an all-sky calculation, using a simulated galaxy cluster or a model magnetized universe obtained from GCMHD+ simulations as the respective input structures. The implications on large-scale magnetic field studies are discussed; remarks on the standard methods using rotation measure are highlighted., Comment: 32 pages, 14 figures

Weak lensing convergence maps - upon which higher order statistics can be calculated - can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic - the peak count as a function of signal to noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well defined confidence levels.

A crucial aspect of mass-mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass-mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artifacts of the reconstruction. Here we present this new formalism, demonstrate the method on simulations, before applying the developed formalism to two observational datasets of the Abel-520 cluster. Initial reconstructions of the Abel-520 catalogs reported the detection of an anomalous 'dark core' -- an over dense region with no optical counterpart -- which was taken to be evidence for self-interacting dark-matter. In our Bayesian framework it is found that neither Abel-520 dataset can conclusively determine the physicality of such dark cores at 99% confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

Until recently mass-mapping techniques for weak gravitational lensing convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstruction uncertainties, without making strong assumptions of Gaussianity. In previous work we presented a sparse hierarchical Bayesian formalism for convergence reconstruction that addresses this shortcoming. Here, we draw on the concept of local credible intervals (cf. Bayesian error bars) as an extension of the uncertainty quantification techniques previously detailed. These uncertainty quantification techniques are benchmarked against those recovered via Px-MALA - a state of the art proximal Markov Chain Monte Carlo (MCMC) algorithm. We find that typically our recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated (Pearson correlation coefficient $\geq 0.85$) with those recovered via Px-MALA. Moreover, we demonstrate an increase in computational efficiency of $\mathcal{O}(10^6)$ when using our sparse Bayesian approach over MCMC techniques. This computational saving is critical for the application of Bayesian uncertainty quantification to large-scale stage IV surveys such as LSST and Euclid.

Upcoming experiments such as the SKA will provide huge quantities of data. Fast modelling of the high-redshift 21cm signal will be crucial for efficiently comparing these data sets with theory. The most detailed theoretical predictions currently come from numerical simulations and from faster but less accurate semi-numerical simulations. Recently, machine learning techniques have been proposed to emulate the behaviour of these semi-numerical simulations with drastically reduced time and computing cost. We compare the viability of five such machine learning techniques for emulating the 21cm power spectrum of the publicly-available code SimFast21. Our best emulator is a multilayer perceptron with three hidden layers, reproducing SimFast21 power spectra $10^8$ times faster than the simulation with 4% mean squared error averaged across all redshifts and input parameters. The other techniques (interpolation, Gaussian processes regression, and support vector machine) have slower prediction times and worse prediction accuracy than the multilayer perceptron. All our emulators can make predictions at any redshift and scale, which gives more flexible predictions but results in significantly worse prediction accuracy at lower redshifts. We then present a proof-of-concept technique for mapping between two different simulations, exploiting our best emulator's fast prediction speed. We demonstrate this technique to find a mapping between SimFast21 and another publicly-available code 21cmFAST. We observe a noticeable offset between the simulations for some regions of the input space. Such techniques could potentially be used as a bridge between fast semi-numerical simulations and accurate numerical radiative transfer simulations., Comment: 17 pages, 14 figures

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 co-moving distance, r(z). We find that lensing predominately constrains a single global power spectrum amplitude and several co-moving distance bins. Our approach can localise precise scales and redshifts where Lambda-Cold Dark Matter (LCDM) fails -- if any. We find that below z = 0.4, the measured co-moving distance r (z) is higher than that expected from the Planck LCDM cosmology by ~1.5 sigma, 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 non-parametric information and we find good agreement., Comment: 13 pages. Matches PRD accepted version

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 = 7 h /Mpc This requirement is not absolute since the bias depends on the magnitude of modelling 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 modelling scenarios and introduce a general formalism and public code, RequiSim, to compute the expected bias from any non-linear model., Comment: 17 pages, 13 figures. Accepted and published in PRD

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., Comment: Phys. Rev. D. accepted. 6 pages, 2 figures

The Large Synoptic Survey Telescope is designed to provide an unprecedented optical imaging dataset that will support investigations of our Solar System, Galaxy and Universe, across half the sky and over ten years of repeated observation. However, exactly how the LSST observations will be taken (the observing strategy or "cadence") is not yet finalized. In this dynamically-evolving community white paper, we explore how the detailed performance of the anticipated science investigations is expected to depend on small changes to the LSST observing strategy. Using realistic simulations of the LSST schedule and observation properties, we design and compute diagnostic metrics and Figures of Merit that provide quantitative evaluations of different observing strategies, analyzing their impact on a wide range of proposed science projects. This is work in progress: we are using this white paper to communicate to each other the relative merits of the observing strategy choices that could be made, in an effort to maximize the scientific value of the survey. The investigation of some science cases leads to suggestions for new strategies that could be simulated and potentially adopted. Notably, we find motivation for exploring departures from a spatially uniform annual tiling of the sky: focusing instead on different parts of the survey area in different years in a "rolling cadence" is likely to have significant benefits for a number of time domain and moving object astronomy projects. The communal assembly of a suite of quantified and homogeneously coded metrics is the vital first step towards an automated, systematic, science-based assessment of any given cadence simulation, that will enable the scheduling of the LSST to be as well-informed as possible., Comment: 312 pages, 90 figures. Browse the current version at https://github.com/LSSTScienceCollaborations/ObservingStrategy, new contributions welcome!

Convergence maps of the integrated matter distribution are a key science result from weak gravitational lensing surveys. To date, recovering convergence maps has been performed using a planar approximation of the celestial sphere. However, with the increasing area of sky covered by dark energy experiments, such as Euclid, the Large Synoptic Survey Telescope (LSST), and the Wide Field Infrared Survey Telescope (WFIRST), this assumption will no longer be valid. We recover convergence fields on the celestial sphere using an extension of the Kaiser-Squires estimator to the spherical setting. Through simulations we study the error introduced by planar approximations. Moreover, we examine how best to recover convergence maps in the planar setting, considering a variety of different projections and defining the local rotations that are required when projecting spin fields such as cosmic shear. For the sky coverages typical of future surveys, errors introduced by projection effects can be of order tens of percent, exceeding 50% in some cases. The stereographic projection, which is conformal and so preserves local angles, is the most effective planar projection. In any case, these errors can be avoided entirely by recovering convergence fields directly on the celestial sphere. We apply the spherical Kaiser-Squires mass-mapping method presented to the public Dark Energy Survey (DES) science verification data to recover convergence maps directly on the celestial sphere., Comment: 18 Pages, 10 Figures, comments welcome, code will made publicly available until then is available on request

In this paper we discuss the commonly-used limiting cases, or approximations, for two-point cosmic shear statistics. We discuss the most prominent assumptions in this statistic: the flat-sky (small angle limit), the Limber (Bessel-to-delta function limit) and the Hankel transform (large l-mode limit) approximations; that the vast majority of cosmic shear results to date have used simultaneously. We find that the combined effect of these approximations can suppress power by >1% on scales of l<40. A fully non-approximated cosmic shear study should use a spherical-sky, non-Limber-approximated power spectrum analysis; and a transform involving Wigner small-d matrices in place of the Hankel transform. These effects, unaccounted for, would constitute at least 11% of the total budget for systematic effects for a power spectrum analysis of a Euclid-like experiment; but they are unnecessary., Comment: 15 pages, accepted to MNRAS

A fundamental assumption in the standard model of cosmology is that the Universe is isotropic on large scales. Breaking this assumption leads to a set of solutions to Einstein's field equations, known as Bianchi cosmologies, only a subset of which have ever been tested against data. For the first time, we consider all degrees of freedom in these solutions to conduct a general test of isotropy using cosmic microwave background temperature and polarization data from Planck. For the vector mode (associated with vorticity), we obtain a limit on the anisotropic expansion of $(\sigma_V/H)_0 < 4.7 \times 10^{-11}$ (95% CI), which is an order of magnitude tighter than previous Planck results that used CMB temperature only. We also place upper limits on other modes of anisotropic expansion, with the weakest limit arising from the regular tensor mode, $(\sigma_{T,\rm reg}/H)_0<1.0 \times 10^{-6}$ (95% CI). Including all degrees of freedom simultaneously for the first time, anisotropic expansion of the Universe is strongly disfavoured, with odds of 121,000:1 against., Comment: 6 pages, 1 figure, v2: replaced with version accepted by PRL

We present new methods for mapping the curl-free (E-mode) and divergence-free (B-mode) components of spin 2 signals using spin directional wavelets. Our methods are equally applicable to measurements of the polarisation of the cosmic microwave background (CMB) and the shear of galaxy shapes due to weak gravitational lensing. We derive pseudo and pure wavelet estimators, where E-B mixing arising due to incomplete sky coverage is suppressed in wavelet space using scale- and orientation-dependent masking and weighting schemes. In the case of the pure estimator, ambiguous modes (which have vanishing curl and divergence simultaneously on the incomplete sky) are also cancelled. On simulations, we demonstrate the improvement (i.e., reduction in leakage) provided by our wavelet space estimators over standard harmonic space approaches. Our new methods can be directly interfaced in a coherent and computationally-efficient manner with component separation or feature extraction techniques that also exploit wavelets., Comment: 13 pages, MNRAS accepted. Companion paper: K. Rogers et al., "Spin-SILC: CMB polarisation component separation with spin wavelets", in this ArXiv mailing

We present Spin-SILC, a new foreground component separation method that accurately extracts the cosmic microwave background (CMB) polarisation $E$ and $B$ modes from raw multifrequency Stokes $Q$ and $U$ measurements of the microwave sky. Spin-SILC is an internal linear combination method that uses spin wavelets to analyse the spin-2 polarisation signal $P = Q + iU$. The wavelets are additionally directional (non-axisymmetric). This allows different morphologies of signals to be separated and therefore the cleaning algorithm is localised using an additional domain of information. The advantage of spin wavelets over standard scalar wavelets is to simultaneously and self-consistently probe scales and directions in the polarisation signal $P = Q + iU$ and in the underlying $E$ and $B$ modes, therefore providing the ability to perform component separation and $E$-$B$ decomposition concurrently for the first time. We test Spin-SILC on full-mission Planck simulations and data and show the capacity to correctly recover the underlying cosmological $E$ and $B$ modes. We also demonstrate a strong consistency of our CMB maps with those derived from existing component separation methods. Spin-SILC can be combined with the pseudo- and pure $E$-$B$ spin wavelet estimators presented in a companion paper to reliably extract the cosmological signal in the presence of complicated sky cuts and noise. Therefore, it will provide a computationally-efficient method to accurately extract the CMB $E$ and $B$ modes for future polarisation experiments., Comment: 13 pages, 9 figures. Minor changes to match version published in MNRAS. Map products available at http://www.silc-cmb.org. Companion paper: arXiv:1605.01414 "Wavelet reconstruction of pure E and B modes for CMB polarisation and cosmic shear analyses" (B. Leistedt et al.)

We present a new framework for testing the isotropy of the Universe using cosmic microwave background data, building on the nested-sampling ANICOSMO code. Uniquely, we are able to constrain the scalar, vector and tensor degrees of freedom alike; previous studies only considered the vector mode (linked to vorticity). We employ Bianchi type VII$_h$ cosmologies to model the anisotropic Universe, from which other types may be obtained by taking suitable limits. In a separate development, we improve the statistical analysis by including the effect of Bianchi power in the high-$\ell$, as well as the low-$\ell$, likelihood. To understand the effect of all these changes, we apply our new techniques to WMAP data. We find no evidence for anisotropy, constraining shear in the vector mode to $(\sigma_V/H)_0 < 1.7 \times 10^{-10}$ (95% CL). For the first time, we place limits on the tensor mode; unlike other modes, the tensor shear can grow from a near-isotropic early Universe. The limit on this type of shear is $(\sigma_{T,\rm reg}/H)_0 < 2.4 \times 10^{-7}$ (95% CL)., Comment: 11 pages, 6 figures, v3: minor modifications to match version accepted by MNRAS

Automated photometric supernova classification has become an active area of research in recent years in light of current and upcoming imaging surveys such as the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope, given that spectroscopic confirmation of type for all supernovae discovered will be impossible. Here, we develop a multi-faceted classification pipeline, combining existing and new approaches. Our pipeline consists of two stages: extracting descriptive features from the light curves and classification using a machine learning algorithm. Our feature extraction methods vary from model-dependent techniques, namely SALT2 fits, to more independent techniques fitting parametric models to curves, to a completely model-independent wavelet approach. We cover a range of representative machine learning algorithms, including naive Bayes, k-nearest neighbors, support vector machines, artificial neural networks and boosted decision trees (BDTs). We test the pipeline on simulated multi-band DES light curves from the Supernova Photometric Classification Challenge. Using the commonly used area under the curve (AUC) of the Receiver Operating Characteristic as a metric, we find that the SALT2 fits and the wavelet approach, with the BDTs algorithm, each achieves an AUC of 0.98, where 1 represents perfect classification. We find that a representative training set is essential for good classification, whatever the feature set or algorithm, with implications for spectroscopic follow-up. Importantly, we find that by using either the SALT2 or the wavelet feature sets with a BDT algorithm, accurate classification is possible purely from light curve data, without the need for any redshift information., Comment: Matches published version. 15 pages, 7 figures

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 wavelet ILC or SILC. Directional wavelets, when convolved with signals on the sphere, can separate the anisotropic filamentary structures which are characteristic of both the CMB and foregrounds. Extending previous component separation methods, which use the frequency, spatial and harmonic signatures of foregrounds to separate them from the cosmological background signal, SILC can additionally use morphological information in the foregrounds and CMB to better localise the cleaning algorithm. We test the method on Planck data and simulations, demonstrating consistency with existing component separation algorithms, and discuss how to optimise the use of morphological information by varying the number of directional wavelets as a function of spatial scale. We find that combining the use of directional and axisymmetric wavelets depending on scale could yield higher quality CMB temperature maps. Our results set the stage for the application of SILC to polarisation anisotropies through an extension to spin wavelets., Comment: 15 pages, 13 figures. Minor changes to match version published in MNRAS. Map products available at http://www.silc-cmb.org

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 of 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 information. 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., Comment: 24 pages, 4 figures, version accepted for publication in PRD

We discuss a new scale-discretised directional wavelet transform to analyse spin signals defined on the sphere, in particular the polarisation of the cosmic microwave background (CMB)., Comment: 1 page, Proceedings of International BASP Frontiers Workshop 2015

Over the past few years two of the largest and highest fidelity experiments conceived have been approved for construction: Euclid is an ESA M-Class mission that will map three-quarters of the extra galactic sky with Hubble Space Telescope resolution optical and NIR imaging, and NIR spectroscopy, its scientific aims (amongst others) are to create a map of the dark Universe and to determine the nature of dark energy. The Square Kilometre Array (SKA) has similar scientific aims (and others) using radio wavelength observations. The two experiments are synergistic in several respects, both through the scientific objectives and through the control of systematic effects. SKA Phase-1 and Euclid will be commissioned on similar timescales offering an exciting opportunity to exploit synergies between these facilities., Comment: This article is part of the 'SKA Synergies Chapter, Advancing Astrophysics with the SKA (AASKA14) Conference, Giardini Naxos (Italy), June 9th-13th 2014'

A new spin wavelet transform on the sphere is proposed to analyse the polarisation of the cosmic microwave background (CMB), a spin $\pm 2$ signal observed on the celestial sphere. The scalar directional scale-discretised wavelet transform on the sphere is extended to analyse signals of arbitrary spin. The resulting spin scale-discretised wavelet transform probes the directional intensity of spin signals. A procedure is presented using this new spin wavelet transform to recover E- and B-mode signals from partial-sky observations of CMB polarisation., Comment: 4 pages, Proceedings IAU Symposium No. 306, 2014 (A. F. Heavens, J.-L. Starck, A. Krone-Martins eds.)

We present a novel, general-purpose method for deconvolving and denoising images from gridded radio interferometric visibilities using Bayesian inference based on a Gaussian process model. The method automatically takes into account incomplete coverage of the uv-plane, signal mode coupling due to the primary beam, and noise mode coupling due to uv sampling. Our method uses Gibbs sampling to efficiently explore the full posterior distribution of the underlying signal image given the data. We use a set of widely diverse mock images with a realistic interferometer setup and level of noise to assess the method. Compared to results from a proxy for point source- based CLEAN method we find that in terms of RMS error and signal-to-noise ratio our approach performs better than traditional deconvolution techniques, regardless of the structure of the source image in our test suite. Our implementation scales as O(np log np), provides full statistical and uncertainty information of the reconstructed image, requires no supervision, and provides a robust, consistent framework for incorporating noise and parameter marginalizations and foreground removal., Comment: 12 pages, 10 figures, MNRAS accepted. arXiv admin note: text overlap with arXiv:1109.4640