# ProfessorAlanHeavens

Faculty of Natural SciencesDepartment of Physics

Chair in Astrostatistics

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### Contact

+44 (0)20 7594 2930a.heavens

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### Location

1018EBlackett LaboratorySouth Kensington Campus

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## Publications

Publication Type
Year
to

221 results found

Mootoovaloo A, Jaffe AH, Heavens AF, Leclercq Fet al., 2021, Kernel-based emulator for the 3D matter power spectrum from CLASS, Astronomy and Computing, Pages: 100508-100508, ISSN: 2213-1337

Journal article

Berera A, Brahma S, Brandenberger R, Calderon-Figueroa J, Heavens Aet al., 2021, Quantum coherence of photons to cosmological distances, PHYSICAL REVIEW D, Vol: 104, ISSN: 2470-0010

Journal article

Di Valentino E, Anchordoqui LA, Akarsu O, Ali-Haimoud Y, Amendola L, Arendse N, Asgari M, Ballardini M, Basilakos S, Battistelli E, Benetti M, Birrer S, Bouchet FR, Bruni M, Calabrese E, Camarena D, Capozziello S, Chen A, Chluba J, Chudaykin A, Colgain EO, Cyr-Racine F-Y, de Bernardis P, Perez JDC, Delabrouille J, Dunkley J, Escamilla-Rivera C, Ferte A, Finelli F, Freedman W, Frusciante N, Giusarma E, Gomez-Valent A, Guy J, Handley W, Harrison I, Hart L, Heavens A, Hildebrandt H, Holz D, Huterer D, Ivanov MM, Joudaki S, Kamionkowski M, Karwal T, Knox L, Kumar S, Lamagna L, Lesgourgues J, Lucca M, Marra V, Masi S, Matarrese S, Mazumdar A, Melchiorri A, Mena O, Mersini-Houghton L, Miranda V, Moreno-Pulido C, Mota DF, Muir J, Mukherjee A, Niedermann F, Notari A, Nunes RC, Pace F, Paliathanasis A, Palmese A, Pan S, Paoletti D, Pettorino V, Piacentini F, Poulin V, Raveri M, Riess AG, Salzano V, Saridakis EN, Sen AA, Shafieloo A, Shajib AJ, Silk J, Silvestri A, Sloth MS, Smith TL, Peracaula JS, van de Bruck C, Verde L, Visinelli L, Wandelta BD, Wang D, Wang J-M, Yadav AK, Yang Wet al., 2021, Snowmass2021-Letter of interest cosmology intertwined II: The hubble constant tension, ASTROPARTICLE PHYSICS, Vol: 131, ISSN: 0927-6505

Journal article

Di Valentino E, Anchordoqui LA, Akarsu O, Ali-Haimoud Y, Amendola L, Arendse N, Asgari M, Ballardini M, Basilakos S, Battistelli E, Benetti M, Birrer S, Bouchet FR, Bruni M, Calabrese E, Camarena D, Capozziello S, Chen A, Chluba J, Chudaykin A, Colgain EO, Cyr-Racine F-Y, de Bernardis P, de Cruz Perez J, Delabrouille J, Escamilla-Rivera C, Ferte A, Finelli F, Freedman W, Frusciante N, Giusarma E, Gomez-Valent A, Handley W, Harrison I, Hart L, Heavens A, Hildebrandt H, Holz D, Huterer D, Ivanov MM, Joudaki S, Kamionkowski M, Karwal T, Knox L, Kumar S, Lamagna L, Lesgourgues J, Lucca M, Marra V, Masi S, Matarrese S, Mazumdar A, Melchiorri A, Mena O, Mersini-Houghton L, Miranda V, Moreno-Pulido C, Mota DF, Muir J, Mukherjee A, Niedermann F, Notari A, Nunes RC, Pace F, Paliathanasis A, Palmese A, Pan S, Paoletti D, Pettorino V, Piacentini F, Poulin V, Raveri M, Riess AG, Salzano V, Saridakis EN, Sen AA, Shafieloo A, Shajib AJ, Silk J, Silvestri A, Sloth MS, Smith TL, Sola Peracaula J, van de Bruck C, Verde L, Visinelli L, Wandelt BD, Wang D, Wang J-M, Yadav AK, Yang Wet al., 2021, Snowmass2021-Letter of interest cosmology intertwined IV: The age of the universe and its curvature, ASTROPARTICLE PHYSICS, Vol: 131, ISSN: 0927-6505

Journal article

Di Valentino E, Anchordoqui LA, Akarsu O, Ali-Haimoud Y, Amendola L, Arendse N, Asgari M, Ballardini M, Basilakos S, Battistelli E, Benetti M, Birrer S, Bouchet FR, Bruni M, Calabrese E, Camarena D, Capozziello S, Chen A, Chluba J, Chudaykin A, Colgain EO, Cyr-Racine F-Y, de Bernardis P, Perez JDC, Delabrouille J, Dunkley J, Escamilla-Rivera C, Ferte A, Finelli F, Freedman W, Frusciante N, Giusarma E, Gomez-Valent A, Handley W, Harrison I, Hart L, Heavens A, Hildebrandt H, Holz D, Huterer D, Ivanov MM, Joudaki S, Kamionkowski M, Karwal T, Knox L, Kumar S, Lamagna L, Lesgourgues J, Lucca M, Marra V, Masi S, Matarrese S, Mazumdar A, Melchiorri A, Mena O, Mersini-Houghton L, Miranda V, Moreno-Pulido C, Mota DF, Muir J, Mukherjee A, Niedermann F, Notari A, Nunes RC, Pace F, Paliathanasisa A, Palmese A, Pan S, Paoletti D, Pettorino V, Piacentini F, Poulin V, Raveri M, Riess AG, Salzano V, Saridakis EN, Sen AA, Shafieloo A, Shajib AJ, Silkb J, Silvestri A, Sloth MS, Smith TL, Peracaula JS, van de Bruck C, Verde L, Visinelli L, Wandeltb BD, Wang D, Wang J-M, Yadav AK, Yang Wet al., 2021, Snowmass2021-Letter of interest cosmology intertwined I: Perspectives for the next decade, ASTROPARTICLE PHYSICS, Vol: 131, ISSN: 0927-6505

Journal article

Di Valentino E, Anchordoqui LA, Akarsu O, Ali-Haimoud Y, Amendola L, Arendse N, Asgari M, Ballardini M, Basilakos S, Battistelli E, Benetti M, Birrer S, Bouchet FR, Bruni M, Calabrese E, Camarena D, Capozziello S, Chen A, Chluba J, Chudaykin A, Colgain EO, Cyr-Racine F-Y, de Bernardis P, Perez JDC, Delabrouille J, Dunkley J, Escamilla-Rivera C, Ferte A, Finelli F, Freedman W, Frusciante N, Giusarma E, Gomez-Valent A, Handley W, Harrison I, Hart L, Heavens A, Hildebrandt H, Holz D, Huterer D, Ivanov MM, Joudaki S, Kamionkowski M, Karwal T, Knox L, Kumar S, Lamagna L, Lesgourgues J, Lucca M, Marra V, Masi S, Matarrese S, Mazumdar A, Melchiorri A, Mena O, Mersini-Houghton L, Miranda V, Moreno-Pulido C, Mota DF, Muir J, Mukherjee A, Niedermann F, Notari A, Nunes RC, Pace F, Paliathanasis A, Palmese A, Pan S, Paoletti D, Pettorino V, Piacentini F, Poulin V, Raveri M, Riess AG, Salzano V, Saridakis EN, Sen AA, Shafieloo A, Shajib AJ, Silk J, Silvestri A, Sloth MS, Smith TL, Sola J, van de Bruck C, Verde L, Visinelli L, Wandelt BD, Wang D, Wang J-M, Yadav AK, Yang Wet al., 2021, Cosmology intertwined III: f sigma(8) and S-8, ASTROPARTICLE PHYSICS, Vol: 131, ISSN: 0927-6505

Journal article

Leclercq F, Heavens A, 2021, On the accuracy and precision of correlation functions and field-level inference in cosmology, Monthly Notices of the Royal Astronomical Society, ISSN: 0035-8711

We present a comparative study of the accuracy and precision of correlationfunction methods and full-field inference in cosmological data analysis. To doso, we examine a Bayesian hierarchical model that predicts log-normal fieldsand their two-point correlation function. Although a simplified analytic model,the log-normal model produces fields that share many of the essentialcharacteristics of the present-day non-Gaussian cosmological density fields. Weuse three different statistical techniques: (i) a standard likelihood-basedanalysis of the two-point correlation function; (ii) a likelihood-free(simulation-based) analysis of the two-point correlation function; (iii) afield-level analysis, made possible by the more sophisticated data assimilationtechnique. We find that (a) standard assumptions made to write down alikelihood for correlation functions can cause significant biases, a problemthat is alleviated with simulation-based inference; and (b) analysing theentire field offers considerable advantages over correlation functions, throughhigher accuracy, higher precision, or both. The gains depend on the degree ofnon-Gaussianity, but in all cases, including for weak non-Gaussianity, theadvantage of analysing the full field is substantial.

Journal article

Jung G, Namikawa T, Liguori M, Munshi D, Heavens Aet al., 2021, The integrated angular bispectrum of weak lensing, Journal of Cosmology and Astroparticle Physics, Vol: 2021, Pages: 1-22, ISSN: 1475-7516

We investigate three-point statistics in weak lensing convergence, through the integrated bispectrum. This statistic involves measuring power spectra in patches, and is thus easy to measure, and avoids the complexity of estimating the very large number of possible bispectrum configurations. The integrated bispectrum principally probes the squeezed limit of the bispectrum. To be useful as a set of summary statistics, accurate theoretical predictions of the signal are required, and, assuming Gaussian sampling distributions, the covariance matrix. In this paper, we investigate through simulations how accurate are theoretical formulae for both the integrated bispectrum and its covariance, finding that there a small inaccuracies in the theoretical signal, and more serious deviations in the covariance matrix, which may need to be estimated using simulations.

Journal article

Porqueres N, Heavens A, Mortlock D, Lavaux Get al., 2021, Bayesian forward modelling of cosmic shear data, Monthly Notices of the Royal Astronomical Society, Vol: 502, Pages: 3035-3044, ISSN: 0035-8711

We present a Bayesian hierarchical modelling approach to infer the cosmic matter density field, and the lensing and the matter power spectra, from cosmic shear data. This method uses a physical model of cosmic structure formation to infer physically plausible cosmic structures, which accounts for the non-Gaussian features of the gravitationally evolved matter distribution and light-cone effects. We test and validate our framework with realistic simulated shear data, demonstrating that the method recovers the unbiased matter distribution and the correct lensing and matter power spectrum. While the cosmology is fixed in this test, and the method employs a prior power spectrum, we demonstrate that the lensing results are sensitive to the true power spectrum when this differs from the prior. In this case, the density field samples are generated with a power spectrum that deviates from the prior, and the method recovers the true lensing power spectrum. The method also recovers the matter power spectrum across the sky, but as currently implemented, it cannot determine the radial power since isotropy is not imposed. In summary, our method provides physically plausible inference of the dark matter distribution from cosmic shear data, allowing us to extract information beyond the two-point statistics and exploiting the full information content of the cosmological fields.

Journal article

Heavens A, Sellentin E, Jaffe A, 2020, Extreme data compression while searching for new physics, Monthly Notices of the Royal Astronomical Society, Vol: 498, Pages: 3440-3451, ISSN: 0035-8711

Bringing a high-dimensional dataset into science-ready shape is a formidablechallenge that often necessitates data compression. Compression has accordinglybecome a key consideration for contemporary cosmology, affecting public datareleases, and reanalyses searching for new physics. However, data compressionoptimized for a particular model can suppress signs of new physics, or evenremove them altogether. We therefore provide a solution for exploring newphysics \emph{during} data compression. In particular, we store additionalagnostic compressed data points, selected to enable precise constraints ofnon-standard physics at a later date. Our procedure is based on the maximalcompression of the MOPED algorithm, which optimally filters the data withrespect to a baseline model. We select additional filters, based on ageneralised principal component analysis, which are carefully constructed toscout for new physics at high precision and speed. We refer to the augmentedset of filters as MOPED-PC. They enable an analytic computation of Bayesianevidences that may indicate the presence of new physics, and fast analyticestimates of best-fitting parameters when adopting a specific non-standardtheory, without further expensive MCMC analysis. As there may be large numbersof non-standard theories, the speed of the method becomes essential. Should nonew physics be found, then our approach preserves the precision of the standardparameters. As a result, we achieve very rapid and maximally preciseconstraints of standard and non-standard physics, with a technique that scaleswell to large dimensional datasets.

Journal article

Jimenez R, Heavens AF, 2020, The distribution of dark galaxies and spin bias, Monthly Notices of the Royal Astronomical Society, Vol: 498, Pages: L93-L97, ISSN: 0035-8711

In the light of the discovery of numerous (almost) dark galaxies from the ALFALAFA and LITTLE THINGS surveys, we revisit the predictions of Jimenez et al. 1997, based on the Toomre stability of rapidly-spinning gas disks. We have updated the predictions for ΛCDM with parameters given by Planck18, computing the expected number densities of dark objects, and their spin parameter and mass distributions. Comparing with the data is more challenging, but where the spins are more reliably determined, the spins are close to the threshold for disks to be stable according to the Toomre criterion, where the expected number density is highest, and reinforces the concept that there is a bias in the formation of luminous galaxies based on the spin of their parent halo.

Journal article

Mootoovaloo A, Heavens AF, Jaffe AH, Leclercq Fet al., 2020, Parameter Inference for Weak Lensing using Gaussian Processes and MOPED, Monthly Notices of the Royal Astronomical Society, Vol: 497, Pages: 2213-2226, ISSN: 0035-8711

In this paper, we propose a Gaussian Process (GP) emulator for the calculation both of tomographic weak lensing band powers, and of coefficients of summary data massively compressed with the MOPED algorithm. In the former case cosmological parameter inference is accelerated by a factor of ∼10–30 compared with Boltzmann solver class applied to KiDS-450 weak lensing data. Much larger gains of order 103 will come with future data, and MOPED with GPs will be fast enough to permit the Limber approximation to be dropped, with acceleration in this case of ∼105. A potential advantage of GPs is that an error on the emulated function can be computed and this uncertainty incorporated into the likelihood. However, it is known that the GP error can be unreliable when applied to deterministic functions, and we find, using the Kullback–Leibler divergence between the emulator and class likelihoods, and from the uncertainties on the parameters, that agreement is better when the GP uncertainty is not used. In future, weak lensing surveys such as Euclid, and the Legacy Survey of Space and Time, will have up to ∼104 summary statistics, and inference will be correspondingly more challenging. However, since the speed of MOPED is determined not the number of summary data, but by the number of parameters, MOPED analysis scales almost perfectly, provided that a fast way to compute the theoretical MOPED coefficients is available. The GP provides such a fast mechanism.

Journal article

Leclercq F, Faure B, Lavaux G, Wandelt BD, Jaffe AH, Heavens AF, Percival WJ, Noûs Cet al., 2020, Perfectly parallel cosmological simulations using spatial comoving Lagrangian acceleration, Astronomy and Astrophysics: a European journal, Vol: 639, ISSN: 0004-6361

Context. Existing cosmological simulation methods lack a high degree of parallelism due to the long-range nature of the gravitational force, which limits the size of simulations that can be run at high resolution.Aims. To solve this problem, we propose a new, perfectly parallel approach to simulate cosmic structure formation, which is based on the spatial COmoving Lagrangian Acceleration (sCOLA) framework.Methods. Building upon a hybrid analytical and numerical description of particles’ trajectories, our algorithm allows for an efficient tiling of a cosmological volume, where the dynamics within each tile is computed independently. As a consequence, the degree of parallelism is equal to the number of tiles. We optimised the accuracy of sCOLA through the use of a buffer region around tiles and of appropriate Dirichlet boundary conditions around sCOLA boxes.Results. As a result, we show that cosmological simulations at the degree of accuracy required for the analysis of the next generation of surveys can be run in drastically reduced wall-clock times and with very low memory requirements.Conclusions. The perfect scalability of our algorithm unlocks profoundly new possibilities for computing larger cosmological simulations at high resolution, taking advantage of a variety of hardware architectures.

Journal article

Leclercq F, Enzi W, Jasche J, Heavens Aet al., 2019, Primordial power spectrum and cosmology from black-box galaxy surveys, Monthly Notices of the Royal Astronomical Society, Vol: 490, Pages: 4237-4253, ISSN: 0035-8711

We propose a new, likelihood-free approach to inferring the primordial matterpower spectrum and cosmological parameters from arbitrarily complex forwardmodels of galaxy surveys where all relevant statistics can be determined fromnumerical simulations, i.e. black-boxes. Our approach builds upon approximateBayesian computation using a novel effective likelihood, and upon thelinearisation of black-box models around an expansion point. Consequently, weobtain simple "filter equations" for an effective posterior of the primordialpower spectrum, and a straightforward scheme for cosmological parameterinference. We demonstrate that the workload is computationally tractable, fixeda priori, and perfectly parallel. As a proof of concept, we apply our frameworkto a realistic synthetic galaxy survey, with a data model accounting forphysical structure formation and incomplete and noisy galaxy observations. Indoing so, we show that the use of non-linear numerical models allows the galaxypower spectrum to be safely fitted up to at least $k_\mathrm{max} = 0.5$$h$/Mpc, outperforming state-of-the-art backward-modelling techniques by afactor of $\sim 5$ in the number of modes used. The result is an unbiasedinference of the primordial matter power spectrum across the entire range ofscales considered, including a high-fidelity reconstruction of baryon acousticoscillations. It translates into an unbiased and robust inference ofcosmological parameters. Our results pave the path towards easy applications oflikelihood-free simulation-based inference in cosmology.

Journal article

Jones DM, Heavens AF, 2019, Gaussian mixture models for blended photometric redshifts, Monthly Notices of the Royal Astronomical Society, Vol: 490, Pages: 3966-3986, ISSN: 0035-8711

Future cosmological galaxy surveys such as the Large Synoptic Survey Telescope (LSST) will photometrically observe very large numbers of galaxies. Without spectroscopy, the redshifts required for the analysis of these data will need to be inferred using photometric redshift techniques that are scalable to large sample sizes. The high number density of sources will also mean that around half are blended. We present a Bayesian photometric redshift method for blended sources that uses Gaussian mixture models to learn the joint flux–redshift distribution from a set of unblended training galaxies, and Bayesian model comparison to infer the number of galaxies comprising a blended source. The use of Gaussian mixture models renders both of these applications computationally efficient and therefore suitable for upcoming galaxy surveys.

Journal article

Jimenez R, Maartens R, Khalifeh AR, Caldwell RR, Heavens AF, Verde Let al., 2019, Measuring the homogeneity of the universe using polarization drift, Journal of Cosmology and Astroparticle Physics, Vol: 2019, ISSN: 1475-7516

We propose a method to probe the homogeneity of a general universe, without assuming symmetry. We show that isotropy can be tested at remote locations on the past lightcone by comparing the line-of-sight and transverse expansion rates, using the time dependence of the polarization of Cosmic Microwave Background photons that have been inverse-Compton scattered by the hot gas in massive clusters of galaxies. This probes a combination of remote transverse and parallel components of the expansion rate of the metric, and we may use radial baryon acoustic oscillations or cosmic clocks to measure the parallel expansion rate. Thus we can test remote isotropy, which is a key requirement of a homogeneous universe. We provide explicit formulas that connect observables and properties of the metric.

Journal article

Schmit CJ, Heavens AF, Pritchard JR, 2019, The gravitational and lensing-ISW bispectrum of 21 cm radiation, Monthly Notices of the Royal Astronomical Society, Vol: 483, Pages: 4259-4275, ISSN: 0035-8711

Cosmic microwave background experiments from COBE to Planck have launched cosmology into an era of precision science, where many cosmological parameters are now determined to the per cent level. Next-generation telescopes, focusing on the cosmological 21 cm signal from neutral hydrogen, will probe enormous volumes in the low-redshift Universe, and have the potential to determine dark energy properties and test modifications of Einstein’s gravity. We study the 21 cm bispectrum due to gravitational collapse as well as the contribution by line-of-sight perturbations in the form of the lensing-ISW bispectrum at low redshifts (⁠z ∼ 0.35−3), targeted by upcoming neutral hydrogen intensity mapping experiments. We compute the expected bispectrum amplitudes and use a Fisher forecast model to compare power spectrum and bispectrum observations of intensity mapping surveys by Canadian Hydrogen Intensity Mapping Experiment (CHIME), MeerKAT, and SKA-mid. We find that combined power spectrum and bispectrum observations have the potential to decrease errors on the cosmological parameters by an order of magnitude compared to Planck. Finally, we compute the contribution of the lensing-ISW bispectrum, and find that, unlike for the cosmic microwave background analyses, it can safely be ignored for 21 cm bispectrum observations.

Journal article

Jones DM, Heavens AF, 2019, Bayesian photometric redshifts of blended sources, Monthly Notices of the Royal Astronomical Society, Vol: 483, Pages: 2487-2505, ISSN: 0035-8711

Photometric redshifts are necessary for enabling large-scale multicolour galaxy surveys to interpret their data and constrain cosmological parameters. While the increased depth of future surveys such as the Large Synoptic Survey Telescope (LSST) will produce higher precision constraints, it will also increase the fraction of sources that are blended. In this paper, we present a Bayesian photometric redshift (BPZ) method for blended sources with an arbitrary number of intrinsic components. This method generalizes existing template-based BPZ methods, and produces joint posterior distributions for the component redshifts that allow uncertainties to be propagated in a principled way. Using Bayesian model comparison, we infer the probability that a source is blended and the number of components that it contains. We extend our formalism to the case where sources are blended in some bands and resolved in others. Applying this to the combination of LSST- and Euclid-like surveys, we find that the addition of resolved photometry results in a significant improvement in the reduction of outliers over the fully blended case. We make available blendz, a Python implementation of our method.

Journal article

Amendola L, Appleby S, Avgoustidis A, Bacon D, Baker T, Baldi M, Bartolo N, Blanchard A, Bonvin C, Borgani S, Branchini E, Burrage C, Camera S, Carbone C, Casarini L, Cropper M, de Rham C, Dietrich JP, Di Porto C, Durrer R, Ealet A, Ferreira PG, Finelli F, Garcia-Bellido J, Giannantonio T, Guzzo L, Heavens A, Heisenberg L, Heymans C, Hoekstra H, Hollenstein L, Holmes R, Hwang Z, Jahnke K, Kitching TD, Koivisto T, Kunz M, La Vacca G, Linder E, March M, Marra V, Martins C, Majerotto E, Markovic D, Marsh D, Marulli F, Massey R, Mellier Y, Montanari F, Mota DF, Nunes NJ, Percival W, Pettorino V, Porciani C, Quercellini C, Read J, Rinaldi M, Sapone D, Sawicki I, Scaramella R, Skordis C, Simpson F, Taylor A, Thomas S, Trotta R, Verde L, Vernizzi F, Vollmer A, Wang Y, Weller J, Zlosnik Tet al., 2018, Cosmology and fundamental physics with the Euclid satellite, Living Reviews in Relativity, Vol: 21, Pages: 1-345, ISSN: 1433-8351

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

Journal article

Jeffrey N, Heavens AF, Fortio PD, 2018, Fast sampling from Wiener posteriors for image data with dataflow engines, Astronomy and Computing, Vol: 25, Pages: 230-237, ISSN: 2213-1337

We use Dataflow Engines (DFE) to construct an efficient Wiener filter of noisy and incomplete image data, and to quickly draw probabilistic samples of the compatible true underlying images from the Wiener posterior. Dataflow computing is a powerful approach using reconfigurable hardware, which can be deeply pipelined and is intrinsically parallel. The unique Wiener-filtered image is the minimum-variance linear estimate of the true image (if the signal and noise covariances are known) and the most probable true image (if the signal and noise are Gaussian distributed). However, many images are compatible with the data with different probabilities, given by the analytic posterior probability distribution referred to as the Wiener posterior. The DFE code also draws large numbers of samples of true images from this posterior, which allows for further statistical analysis. Naive computation of the Wiener-filtered image is impractical for large datasets, as it scales as [Formula presented], where [Formula presented] is the number of pixels. We use a messenger field algorithm, which is well suited to a DFE implementation, to draw samples from the Wiener posterior, that is, with the correct probability we draw samples of noiseless images that are compatible with the observed noisy image. The Wiener-filtered image can be obtained by a trivial modification of the algorithm. We demonstrate a lower bound on the speed-up, from drawing [Formula presented] samples of a [Formula presented] image, of 11.3 ± 0.8 with 8 DFEs in a 1U MPC-X box when compared with a 1U server presenting 32 CPU threads. We also discuss a potential application in astronomy, to provide better dark matter maps and improved determination of the parameters of the Universe.

Journal article

Heavens AF, Di Valentino E, Melchiorri A, Fantaye Yet al., 2018, Bayesian Evidence against Harrison-Zel'dovich spectrum in tension cosmology, Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol: 98, ISSN: 1550-2368

Current cosmological constraints on the scalar spectral index of primordial fluctuations ns in the ΛVcold dark matter (ΛCDM) model have excluded the minimal scale-invariant Harrison-Zel’dovich model (ns=1; hereafter HZ) at high significance, providing support for inflation. In recent years, however, some tensions have emerged between different cosmological data sets that, if not due to systematics, could indicate the presence of new physics beyond the ΛCDM model. In light of these developments, we evaluate the Bayesian evidence against HZ in different data combinations and model extensions. Considering only the Planck temperature data, we find inconclusive evidence against HZ when including variations in the neutrino number Neff and/or the helium abundance YHe. Adding the Planck polarization data, on the other hand, yields strong evidence against HZ in the extensions we considered. Perhaps most interestingly, Planck temperature data combined with local measurements of the Hubble parameter [A. G. Riess et al., Astrophys. J. 826, 56 (2016); A. G. Riess et al. Astrophys. J. 861, 126 (2018)] give as the most probable model a HZ spectrum, with additional neutrinos. However, with the inclusion of polarization, standard ΛCDM is once again preferred, but the HZ model with extra neutrinos is not strongly disfavored. The possibility of fully ruling out the HZ spectrum is therefore ultimately connected with the solution to current tensions between cosmological data sets. If these tensions are confirmed by future data, then new physical mechanisms could be at work and a HZ spectrum could still offer a valid alternative.

Journal article

Heavens AF, Sellentin E, 2018, Objective Bayesian analysis of neutrino masses and hierarchy, Journal of Cosmology and Astroparticle Physics, Vol: 2018, ISSN: 1475-7516

Given the precision of current neutrino data, priors still impact noticeably the constraints on neutrino masses and their hierarchy. To avoid our understanding of neutrinos being driven by prior assumptions, we construct a prior that is mathematically minimally informative. Using the constructed uninformative prior, we find that the normal hierarchy is favoured but with inconclusive posterior odds of 5.1:1. Better data is hence needed before the neutrino masses and their hierarchy can be well constrained. We find that the next decade of cosmological data should provide conclusive evidence if the normal hierarchy with negligible minimum mass is correct, and if the uncertainty in the sum of neutrino masses drops below 0.025 eV. On the other hand, if neutrinos obey the inverted hierarchy, achieving strong evidence will be difficult with the same uncertainties. Our uninformative prior was constructed from principles of the Objective Bayesian approach. The prior is called a reference prior and is minimally informative in the specific sense that the information gain after collection of data is maximised. The prior is computed for the combination of neutrino oscillation data and cosmological data and still applies if the data improve.

Journal article

Heavens A, Alsing J, Jaffe A, Hoffmann T, Kiessling A, Wandelt Bet al., 2017, Bayesian hierarchical modelling of weak lensing - the golden goal, MG14 Meeting on General Relativity, Publisher: World Scientific, Pages: 3005-3010

To accomplish correct Bayesian inference from weak lensing shear datarequires a complete statistical description of the data. The natural frameworkto do this is a Bayesian Hierarchical Model, which divides the chain ofreasoning into component steps. Starting with a catalogue of shear estimates intomographic bins, we build a model that allows us to sample simultaneously fromthe the underlying tomographic shear fields and the relevant power spectra(E-mode, B-mode, and E-B, for auto- and cross-power spectra). The proceduredeals easily with masked data and intrinsic alignments. Using Gibbs samplingand messenger fields, we show with simulated data that the large (over67000-)dimensional parameter space can be efficiently sampled and the fulljoint posterior probability density function for the parameters can feasibly beobtained. The method correctly recovers the underlying shear fields and all ofthe power spectra, including at levels well below the shot noise.

Conference paper

Heavens AF, Sellentin E, 2017, On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak lensing likelihoods, Monthly Notices of the Royal Astronomical Society, Vol: 473, Pages: 2355-2363, ISSN: 0035-8711

We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmologicaldata, is supported by simulated survey data. We define test statistics, based on anovel method that first destroys Gaussian correlations in a data set, and then measures the nonGaussiancorrelations that remain. This procedure flags pairs of data points that depend on eachother in a non-Gaussian fashion, and thereby identifies where the assumption of a Gaussianlikelihood breaks down. Using this diagnosis, we find that non-Gaussian correlations in theCFHTLenS cosmic shear correlation functions are significant. With a simple exclusion of themost contaminated data points, the posterior for s8 is shifted without broadening, but we findno significant reduction in the tension with s8 derived from Planck cosmic microwave backgrounddata. However, we also show that the one-point distributions of the correlation statisticsare noticeably skewed, such that sound weak-lensing data sets are intrinsically likely to leadto a systematically low lensing amplitude being inferred. The detected non-Gaussianities getlarger with increasing angular scale such that for future wide-angle surveys such as Euclidor LSST, with their very small statistical errors, the large-scale modes are expected to beincreasingly affected. The shifts in posteriors may then not be negligible and we recommendthat these diagnostic tests be run as part of future analyses.

Journal article

Heavens AF, Sellentin E, de Mijolla D, Vianello Aet al., 2017, Massive data compression for parameter-dependent covariance matrices, Monthly Notices of the Royal Astronomical Society, Vol: 472, Pages: 4244-4250, ISSN: 0035-8711

We show how the massive data compression algorithm MOPED can be used to reduce, by orders of magnitude, the number of simulated data sets which are required to estimate the covariance matrix required for the analysis of Gaussian-distributed data. This is relevant when the covariance matrix cannot be calculated directly. The compression is especially valuable when the covariance matrix varies with the model parameters. In this case, it may be prohibitively expensive to run enough simulations to estimate the full covariance matrix throughout the parameter space. This compression may be particularly valuable for the next generation of weak lensing surveys, such as proposed for Euclid and Large Synoptic Survey Telescope, for which the number of summary data (such as band power or shear correlation estimates) is very large, ∼104, due to the large number of tomographic redshift bins which the data will be divided into. In the pessimistic case where the covariance matrix is estimated separately for all points in an Monte Carlo Markov Chain analysis, this may require an unfeasible 109 simulations. We show here that MOPED can reduce this number by a factor of 1000, or a factor of ∼106 if some regularity in the covariance matrix is assumed, reducing the number of simulations required to a manageable 103, making an otherwise intractable analysis feasible.

Journal article

Heavens A, Fantaye Y, Sellentin E, Eggers H, Hosenie Z, Kroon S, Mootoovaloo Aet al., 2017, No Evidence for Extensions to the Standard Cosmological Model, PHYSICAL REVIEW LETTERS, Vol: 119, ISSN: 0031-9007

We compute the Bayesian evidence for models considered in the main analysis of Planck cosmic microwave background data. By utilizing carefully defined nearest-neighbor distances in parameter space, we reuse the Monte Carlo Markov chains already produced for parameter inference to compute Bayes factors B for many different model-data set combinations. The standard 6-parameter flat cold dark matter model with a cosmological constant (ΛCDM) is favored over all other models considered, with curvature being mildly favored only when cosmic microwave background lensing is not included. Many alternative models are strongly disfavored by the data, including primordial correlated isocurvature models (lnB=−7.8), nonzero scalar-to-tensor ratio (lnB=−4.3), running of the spectral index (lnB=−4.7), curvature (lnB=−3.6), nonstandard numbers of neutrinos (lnB=−3.1), nonstandard neutrino masses (lnB=−3.2), nonstandard lensing potential (lnB=−4.6), evolving dark energy (lnB=−3.2), sterile neutrinos (lnB=−6.9), and extra sterile neutrinos with a nonzero scalar-to-tensor ratio (lnB=−10.8). Other models are less strongly disfavored with respect to flat ΛCDM. As with all analyses based on Bayesian evidence, the final numbers depend on the widths of the parameter priors. We adopt the priors used in the Planck analysis, while performing a prior sensitivity analysis. Our quantitative conclusion is that extensions beyond the standard cosmological model are disfavored by Planck data. Only when newer Hubble constant measurements are included does ΛCDM become disfavored, and only mildly, compared with a dynamical dark energy model (lnB∼+2).

Journal article

Hikage C, Koyama K, Heavens A, 2017, Perturbation theory for BAO reconstructed fields: One-loop results in the real-space matter density field, PHYSICAL REVIEW D, Vol: 96, ISSN: 2470-0010

We compute the power spectrum at one-loop order in standard perturbation theory for the matter density field to which a standard Lagrangian baryonic acoustic oscillation (BAO) reconstruction technique is applied. The BAO reconstruction method corrects the bulk motion associated with the gravitational evolution using the inverse Zel’dovich approximation (ZA) for the smoothed density field. We find that the overall amplitude of one-loop contributions in the matter power spectrum substantially decreases after reconstruction. The reconstructed power spectrum thereby approaches the initial linear spectrum when the smoothed density field is close enough to linear, i.e., the smoothing scale Rs≳10h−1    Mpc. On smaller Rs, however, the deviation from the linear spectrum becomes significant on large scales (k≲R−1s) due to the nonlinearity in the smoothed density field, and the reconstruction is inaccurate. Compared with N-body simulations, we show that the reconstructed power spectrum at one-loop order agrees with simulations better than the unreconstructed power spectrum. We also calculate the tree-level bispectrum in standard perturbation theory to investigate non-Gaussianity in the reconstructed matter density field. We show that the amplitude of the bispectrum significantly decreases for small k after reconstruction and that the tree-level bispectrum agrees well with N-body results in the weakly nonlinear regime.

Journal article

Kitching TD, Alsing J, Heavens AF, Jimenez R, McEwen JD, Verde Let al., 2017, The limits of cosmic shear, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Vol: 469, Pages: 2737-2749, ISSN: 0035-8711

Journal article

Renzini AI, Contaldi CR, Heavens A, 2017, Mapping weak lensing distortions in the Kerr metric, Physical Review D, Vol: 95, ISSN: 2470-0010

Einstein’s theory of General Relativity implies that energy, i.e., matter, curves space-time and thusdeforms lightlike geodesics, giving rise to gravitational lensing. This phenomenon is well understood in thecase of the Schwarzschild metric and has been accurately described in the past; however, lensing in the Kerrspace-time has received less attention in the literature despite potential practical observational applications.In particular, lensing in such space is not expressible as the gradient of a scalar potential and as such is asource of curl-like signatures and an asymmetric shear pattern. In this paper, we develop a differentiablelensing map in the Kerr metric, reworking and extending previous approaches. By using standard tools ofweak gravitational lensing, we isolate and quantify the distortion that is uniquely induced by the presenceof angular momentum in the metric. We apply this framework to the distortion induced by a Kerr-likeforeground object on a distribution of background of sources. We verify that the new unique lensingsignature is orders of magnitude below current observational bounds for a range of lens configurations.

Journal article

Verde L, Bellini E, Pigozzo C, Heavens AF, Jimenez Ret al., 2017, Early cosmology constrained, JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS, Vol: 2017, ISSN: 1475-7516

We investigate our knowledge of early universe cosmology by exploring how much additional energy density can be placed in different components beyond those in the ΛCDM model. To do this we use a method to separate early- and late-universe information enclosed in observational data, thus markedly reducing the model-dependency of the conclusions. We find that the 95% credibility regions for extra energy components of the early universe at recombination are: non-accelerating additional fluid density parameter ΩMR < 0.006 and extra radiation parameterised as extra effective neutrino species 2.3 < Neff < 3.2 when imposing flatness. Our constraints thus show that even when analyzing the data in this largely model-independent way, the possibility of hiding extra energy components beyond ΛCDM in the early universe is seriously constrained by current observations. We also find that the standard ruler, the sound horizon at radiation drag, can be well determined in a way that does not depend on late-time Universe assumptions, but depends strongly on early-time physics and in particular on additional components that behave like radiation. We find that the standard ruler length determined in this way is rs = 147.4 ± 0.7 Mpc if the radiation and neutrino components are standard, but the uncertainty increases by an order of magnitude when non-standard dark radiation components are allowed, to rs = 150 ± 5 Mpc.

Journal article

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