Publications
228 results found
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.
Heavens AF, Di Valentino E, Melchiorri A, et 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.
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.
Heavens A, Alsing J, Jaffe A, et 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.
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.
Heavens AF, Sellentin E, de Mijolla D, et 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.
Heavens A, Fantaye Y, Sellentin E, et 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).
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.
Kitching TD, Alsing J, Heavens AF, et al., 2017, The limits of cosmic shear, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Vol: 469, Pages: 2737-2749, ISSN: 0035-8711
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.
Verde L, Bellini E, Pigozzo C, et 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.
Kitching TD, Heavens AF, 2017, Unequal-time correlators for cosmology, PHYSICAL REVIEW D, Vol: 95, ISSN: 2470-0010
Measurements of the power spectrum from large-scale structure surveys have, to date, assumed an equal-time approximation, where the full cross-correlation power spectrum of the matter density field evaluated at different times (or distances) has been approximated either by the power spectrum at a fixed time or in an improved fashion, by a geometric mean P(k;r1,r2)=[P(k;r1)P(k;r2)]1/2. In this paper we investigate the expected impact of the geometric mean ansatz and present an application in assessing the impact on weak-gravitational-lensing cosmological parameter inference, using a perturbative unequal time correlator. As one might expect, we find that the impact of this assumption is greatest at large separations in redshift Δz≳0.3 where the change in the amplitude of the matter power spectrum can be as much as 10 percent for k≳5 h Mpc−1. However, of more concern is that the corrections for small separations, where the clustering is not close to zero, may not be negligibly small. In particular, we find that for a Euclid- or LSST-like weak lensing experiment, the assumption of equal-time correlators may result in biased predictions of the cosmic shear power spectrum, and that the impact is strongly dependent on the amplitude of the intrinsic alignment signal. To compute unequal-time correlations to sufficient accuracy will require advances in either perturbation theory to high k modes or extensive use of simulations.
Verde L, Luis Bernal J, Heavens AF, et al., 2017, The length of the low-redshift standard ruler, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Vol: 467, Pages: 731-736, ISSN: 0035-8711
Assuming the existence of standard rulers, standard candles and standard clocks, requiring only the cosmological principle, a metric theory of gravity, a smooth expansion history and using state-of-the-art observations, we determine the length of the ‘low-redshift standard ruler’. The data we use are a compilation of recent baryon acoustic oscillation data (relying on the standard ruler), Type Ia supernovae (as standard candles), ages of early-type galaxies (as standard clocks) and local determinations of the Hubble constant (as a local anchor of the cosmic distance scale). In a standard Λ cold dark matter cosmology, the ‘low-redshift standard ruler’ coincides with the sound horizon at radiation drag, which can also be determined – in a model dependent way – from cosmic microwave background observations. However, in general, the two quantities need not coincide. We obtain constraints on the length of the low-redshift standard ruler: rhs=101.0±2.3h−1rsh=101.0±2.3h−1 Mpc, when using only Type Ia supernovae and baryon acoustic oscillations, and rs = 150.0 ± 4.7 Mpc when using clocks to set the Hubble normalization, while rs = 141.0 ± 5.5 Mpc when using the local Hubble constant determination (using both yields rs = 143.9 ± 3.1 Mpc). The low-redshift determination of the standard ruler has an error, which is competitive with the model-dependent determination from cosmic microwave background measurements made with the Planck satellite, which assumes that it is the sound horizon at the end of baryon drag.
Alsing J, Heavens A, Jaffe AH, 2016, Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Vol: 466, Pages: 3272-3292, ISSN: 0035-8711
We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the Canada–France–Hawaii Telescope (CFHTLenS) weak lensing survey – the first application of this method to data. In the first approach, we sample the joint posterior distribution of the shear maps and power spectra by Gibbs sampling, with minimal model assumptions. In the second approach, we sample the joint posterior of the shear maps and cosmological parameters, providing a new, accurate and principled approach to cosmological parameter inference from cosmic shear data. As a first demonstration on data, we perform a two-bin tomographic analysis to constrain cosmological parameters and investigate the possibility of photometric redshift bias in the CFHTLenS data. Under the baseline ΛCDM (Λ cold dark matter) model, we constrain S8=σ8(Ωm/0.3)0.5=0.67+0.03−0.03S8=σ8(Ωm/0.3)0.5=0.67−0.03+0.03 (68 per cent), consistent with previous CFHTLenS analyses but in tension with Planck. Adding neutrino mass as a free parameter, we are able to constrain ∑mν < 4.6 eV (95 per cent) using CFHTLenS data alone. Including a linear redshift-dependent photo-z bias Δz = p2(z − p1), we find p1=−0.25+0.53−0.60p1=−0.25−0.60+0.53 and p2=−0.15+0.17−0.15p2=−0.15−0.15+0.17 , and tension with Planck is only alleviated under very conservative prior assumptions. Neither the non-minimal neutrino mass nor photo-z bias models are significantly preferred by the CFHTLenS (two-bin tomography) data.
Sellentin E, Heavens AF, 2016, Quantifying lost information due to covariance matrix estimation in parameter inference, Monthly Notices of the Royal Astronomical Society, Vol: 464, Pages: 4658-4665, ISSN: 0035-8711
Parameter inference with an estimated covariance matrix systematically loses information due to the remaining uncertainty of the covariance matrix. Here, we quantify this loss of precision and develop a framework to hypothetically restore it, which allows to judge how far away a given analysis is from the ideal case of a known covariance matrix. We point out that it is insufficient to estimate this loss by debiasing the Fisher matrix as previously done, due to a fundamental inequality that describes how biases arise in non-linear functions. We therefore develop direct estimators for parameter credibility contours and the figure of merit, finding that significantly fewer simulations than previously thought are sufficient to reach satisfactory precisions. We apply our results to DES Science Verification weak lensing data, detecting a 10 per cent loss of information that increases their credibility contours. No significant loss of information is found for KiDS. For a Euclid-like survey, with about 10 nuisance parameters we find that 2900 simulations are sufficient to limit the systematically lost information to 1 per cent, with an additional uncertainty of about 2 per cent. Without any nuisance parameters, 1900 simulations are sufficient to only lose 1 per cent of information. We further derive estimators for all quantities needed for forecasting with estimated covariance matrices. Our formalism allows to determine the sweetspot between running sophisticated simulations to reduce the number of nuisance parameters, and running as many fast simulations as possible.
Ade PAR, Aghanim N, Arnaud M, et al., 2016, Planck 2015 results XVII. Constraints on primordial non-Gaussianity, Astronomy and Astrophysics: a European journal, Vol: 594, ISSN: 0004-6361
The Planck full mission cosmic microwave background (CMB) temperature and E-mode polarization maps are analysed to obtain constraints on primordial non-Gaussianity (NG). Using three classes of optimal bispectrum estimators – separable template-fitting (KSW), binned, and modal – we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result from temperature alone ƒlocalNL = 2.5 ± 5.7, ƒequilNL= -16 ± 70, , and ƒorthoNL = -34 ± 32 (68% CL, statistical). Combining temperature and polarization data we obtain ƒlocalNL = 0.8 ± 5.0, ƒequilNL= -4 ± 43, and ƒorthoNL = -26 ± 21 (68% CL, statistical). The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are consistent with estimators based on measuring the Minkowski functionals of the CMB. The effect of time-domain de-glitching systematics on the bispectrum is negligible. In spite of these test outcomes we conservatively label the results including polarization data as preliminary, owing to a known mismatch of the noise model in simulations and the data. Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the Planck CMB bispectrum and derive constraints on early universe scenarios that generate primordial NG, including general single-field models of inflation, axion inflation, initial state modifications, models producing parity-violating tensor bispectra, and directionally dependent vector models. We present a wide survey of scale-dependent feature and resonance models, accounting for the “look elsewhere” effect in estimating the statistical significance of features. We also look for isocurvature NG, and find no signal, but we obtain constraints tha
Adam R, Ade PAR, Aghanim N, et al., 2016, Planck 2015 results. I. Overview of products and scientific results, Astronomy & Astrophysics, Vol: 594, ISSN: 1432-0746
The European Space Agency’s Planck satellite, which is dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013. In February 2015, ESA and the Planck Collaboration released the second set of cosmology products based ondata from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The data products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing uncertainties and the performance of the analysis methods. The likelihood code used to assess cosmological models against the Planck data is described, along with a CMB lensing likelihood. Scientific results include cosmological parameters derived from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity, and new results on low-frequency Galactic foregrounds.
Ade PAR, Aghanim N, Arnaud M, et al., 2016, Planck 2015 results XIV. Dark energy and modified gravity, ASTRONOMY & ASTROPHYSICS, Vol: 594, ISSN: 1432-0746
We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state w(a), as well as principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints and find that it has to be below ~2% (at 95% confidence) of the critical density, even when forced to play a role for z < 50 only. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories, and coupled DE. In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations (expansion of the equation of state, early DE, general potentials in minimally-coupled scalar fields or principal component analysis) are in agreement with ΛCDM. When testing models that also change perturbations (even when the background is fixed to ΛCDM), some tensions appear in a few scenarios: the maximum one found is ~2σ for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to, at most
Heavens A, 2016, Generalisations of Fisher Matrices, Entropy, Vol: 18, ISSN: 1099-4300
Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters—both their errors and covariances. In this short review, I outline a number of extensions to the simple Fisher matrix formalism, covering a number of recent developments in the field. These are: (a) situations where the data (in the form of ( x,y ) pairs) have errors in both x and y; (b) modifications to parameter inference in the presence of systematic errors, or through fixing the values of some model parameters; (c) Derivative Approximation for LIkelihoods (DALI) - higher-order expansions of the likelihood surface, going beyond the Gaussian shape approximation; (d) extensions of the Fisher-like formalism, to treat model selection problems with Bayesian evidence.
Kitching TD, Verde L, Heavens AF, et al., 2016, Discrepancies between CFHTLenS cosmic shear and Planck: new physics or systematic effects?, Monthly Notices of the Royal Astronomical Society, Vol: 459, Pages: 971-981, ISSN: 1365-2966
There is currently a discrepancy in the measured value of the amplitude of matter clustering, parametrized using σ8, inferred from galaxy weak lensing, and cosmic microwave background (CMB) data, which could be an indication of new physics, such as massive neutrinos or a modification to the gravity law, or baryon feedback. In this paper we make the assumption that the cosmological parameters are well determined by Planck, and use weak lensing data to investigate the implications for baryon feedback and massive neutrinos, as well as possible contributions from intrinsic alignments and biases in photometric redshifts. We apply a non-parametric approach to model the baryonic feedback on the dark matter clustering, which is flexible enough to reproduce the OWLS (OverWhelmingly Large Simulations) and Illustris simulation results. The statistic we use, 3D cosmic shear, is a method that extracts cosmological information from weak lensing data using a spherical-Bessel function power spectrum approach. We analyse the CFHTLenS weak lensing data and, assuming best-fitting cosmological parameters from the Planck CMB experiment, find that there is no evidence for baryonic feedback on the dark matter power spectrum, but there is evidence for a bias in the photometric redshifts in the CFHTLenS data, consistent with a completely independent analysis by Choi et al., based on spectroscopic redshifts, and that these conclusions are robust to assumptions about the intrinsic alignment systematic. We also find an upper limit, of <0.28 eV (1σ), to the sum of neutrino masses conditional on other Λ-cold-dark-matter parameters being fixed.
Munshi D, Hu B, Matsubara T, et al., 2016, Lensing-induced morphology changes in CMB temperature maps in modified gravity theories, Journal of Cosmology and Astroparticle Physics, Vol: 2016, ISSN: 1475-7516
Lensing of the Cosmic Microwave Background (CMB) changes the morphology of pattern of temperature fluctuations, so topological descriptors such as Minkowski Functionals can probe the gravity model responsible for the lensing. We show how the recently introduced two-to-two and three-to-one kurt-spectra (and their associated correlation functions), which depend on the power spectrum of the lensing potential, can be used to probe modified gravity theories such as f(R) theories of gravity and quintessence models. We also investigate models based on effective field theory, which include the constant-Ω model, and low-energy Hořava theories. Estimates of the cumulative signal-to-noise for detection of lensing-induced morphology changes, reaches Script O(103) for the future planned CMB polarization mission COrE+. Assuming foreground removal is possible to ℓmax=3000, we show that many modified gravity theories can be rejected with a high level of significance, making this technique comparable in power to galaxy weak lensing or redshift surveys. These topological estimators are also useful in distinguishing lensing from other scattering secondaries at the level of the four-point function or trispectrum. Examples include the kinetic Sunyaev-Zel'dovich (kSZ) effect which shares, with lensing, a lack of spectral distortion. We also discuss the complication of foreground contamination from unsubtracted point sources.
Bull P, Akrami Y, Adamek J, et al., 2016, Beyond ΛCDM: problems, solutions, and the road ahead, Physics of the Dark Universe, Vol: 12, Pages: 56-99, ISSN: 2212-6864
Despite its continued observational successes, there is a persistent (and growing) interest in extendingcosmology beyond the standard model, ΛCDM. This is motivated by a range of apparently serioustheoretical issues, involving such questions as the cosmological constant problem, the particle nature ofdark matter, the validity of general relativity on large scales, the existence of anomalies in the CMB and onsmall scales, and the predictivity and testability of the inflationary paradigm. In this paper, we summarizethe current status of ΛCDM as a physical theory, and review investigations into possible alternatives alonga number of different lines, with a particular focus on highlighting the most promising directions. Whilethe fundamental problems are proving reluctant to yield, the study of alternative cosmologies has led toconsiderable progress, with much more to come if hopes about forthcoming high-precision observationsand new theoretical ideas are fulfilled.
Sellentin E, Heavens AF, 2016, Parameter inference with estimated covariance matrices, Monthly Notices of the Royal Astronomical Society, Vol: 456, Pages: L132-L136, ISSN: 1365-2966
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be estimated and thereby becomes a random object with some intrinsic uncertainty itself. We show how to infer parameters in the presence of such an estimated covariance matrix, by marginalizing over the true covariance matrix, conditioned on its estimated value. This leads to a likelihood function that is no longer Gaussian, but rather an adapted version of a multivariate t-distribution, which has the same numerical complexity as the multivariate Gaussian. As expected, marginalization over the true covariance matrix improves inference when compared with Hartlap et al.'s method, which uses an unbiased estimate of the inverse covariance matrix but still assumes that the likelihood is Gaussian.
Simpson F, Blake C, Peacock JA, et al., 2016, Galaxy and mass assembly: redshift space distortions from the clipped galaxy field, Physical Review D, Vol: 93, ISSN: 1550-7998
We present the first cosmological measurement derived from a galaxy density field subject to a “clipping” transformation. By enforcing an upper bound on the galaxy number density field in the galaxy and mass assembly survey (GAMA), contributions from the nonlinear processes of virialization and galaxy bias are greatly reduced. This leads to a galaxy power spectrum which is easier to model, without calibration from numerical simulations. We develop a theoretical model for the power spectrum of a clipped field in redshift space, which is exact for the case of anisotropic Gaussian fields. Clipping is found to extend the applicability of the conventional Kaiser prescription by more than a factor of 3 in wave numbers, or a factor of 30 in terms of the number of Fourier modes. By modeling the galaxy power spectrum on scales k<0.3 hMpc−1 and density fluctuations δg<4 we measure the normalized growth rate fσ8(z=0.18)=0.29±0.10.
Duncan CAJ, Heymans C, Heavens AF, et al., 2016, Cluster mass profile reconstruction with size and flux magnification on the HST STAGES survey, Monthly Notices of the Royal Astronomical Society, Vol: 457, Pages: 764-785, ISSN: 1365-2966
We present the first measurement of individual cluster mass estimates using weak lensing size and flux magnification. Using data from the HST STAGES (Space Telescope A901/902 Galaxy Evolution Survey) survey of the A901/902 supercluster we detect the four known groups in the supercluster at high significance using magnification alone. We discuss the application of a fully Bayesian inference analysis, and investigate a broad range of potential systematics in the application of the method. We compare our results to a previous weak lensing shear analysis of the same field finding the recovered signal-to-noise of our magnification-only analysis to range from 45 to 110 per cent of the signal-to-noise in the shear-only analysis. On a case-by-case basis we find consistent magnification and shear constraints on cluster virial radius, and finding that for the full sample, magnification constraints to be a factor 0.77 ± 0.18 lower than the shear measurements.
Alsing J, Heavens A, Jaffe AH, et al., 2015, Hierarchical cosmic shear power spectrum inference, Monthly Notices of the Royal Astronomical Society, Vol: 455, Pages: 4452-4466, ISSN: 1365-2966
We develop a Bayesian hierarchical modelling approach for cosmic shear power spectrum inference, jointly sampling from the posterior distribution of the cosmic shear field and its (tomographic) power spectra. Inference of the shear power spectrum is a powerful intermediate product for a cosmic shear analysis, since it requires very few model assumptions and can be used to perform inference on a wide range of cosmological models a posteriori without loss of information. We show that joint posterior for the shear map and power spectrum can be sampled effectively by Gibbs sampling, iteratively drawing samples from the map and power spectrum, each conditional on the other. This approach neatly circumvents difficulties associated with complicated survey geometry and masks that plague frequentist power spectrum estimators, since the power spectrum inference provides prior information about the field in masked regions at every sampling step. We demonstrate this approach for inference of tomographic shear E-mode, B-mode and EB-cross power spectra from a simulated galaxy shear catalogue with a number of important features; galaxies distributed on the sky and in redshift with photometric redshift uncertainties, realistic random ellipticity noise for every galaxy and a complicated survey mask. The obtained posterior distributions for the tomographic power spectrum coefficients recover the underlying simulated power spectra for both E- and B-modes.
Mead AJ, Peacock JA, Heymans C, et al., 2015, An accurate halo model for fitting non-linear cosmological power spectra and baryonic feedback models, Monthly Notices of the Royal Astronomical Society, Vol: 454, Pages: 1958-1975, ISSN: 1365-2966
We present an optimized variant of the halo model, designed to produce accurate matter power spectra well into the non-linear regime for a wide range of cosmological models. To do this, we introduce physically motivated free parameters into the halo-model formalism and fit these to data from high-resolution N-body simulations. For a variety of Λ cold dark matter (ΛCDM) and wCDM models, the halo-model power is accurate to ≃ 5 per cent for k ≤ 10h Mpc−1 and z ≤ 2. An advantage of our new halo model is that it can be adapted to account for the effects of baryonic feedback on the power spectrum. We demonstrate this by fitting the halo model to power spectra from the OWLS (OverWhelmingly Large Simulations) hydrodynamical simulation suite via parameters that govern halo internal structure. We are able to fit all feedback models investigated at the 5 per cent level using only two free parameters, and we place limits on the range of these halo parameters for feedback models investigated by the OWLS simulations. Accurate predictions to high k are vital for weak-lensing surveys, and these halo parameters could be considered nuisance parameters to marginalize over in future analyses to mitigate uncertainty regarding the details of feedback. Finally, we investigate how lensing observables predicted by our model compare to those from simulations and from halofit for a range of k-cuts and feedback models and quantify the angular scales at which these effects become important. Code to calculate power spectra from the model presented in this paper can be found at https://github.com/alexander-mead/hmcode.
Alsing J, Kirk D, Heavens A, et al., 2015, Weak lensing with sizes, magnitudes and shapes, Monthly Notices of the Royal Astronomical Society, Vol: 452, Pages: 1202-1216, ISSN: 1365-2966
Weak lensing can be observed through a number of effects on the images of distant galaxies; their shapes are sheared, sizes and fluxes (magnitudes) are magnified and positions on the sky are modified by the lensing field. Galaxy shapes probe the shear field whilst size, magnitude and number density probe the convergence field. Both contain cosmological information. In this paper, we are concerned with the magnification of sizes and magnitudes of individual galaxies as a probe of cosmic convergence. We develop a Bayesian approach for inferring the convergence field from measured sizes, magnitudes and redshifts and demonstrate that this inference requires detailed knowledge of the joint distribution of intrinsic sizes and magnitudes. We build a simple parametrized model for the size–magnitude distribution and estimate this distribution for CFHTLenS galaxies. In light of the measured distribution, we show that the typical dispersion on convergence estimation is ∼0.8, compared to ∼0.38 for shear. We discuss the possibility of physical systematics for magnification (similar to intrinsic alignments for shear) and compute the expected gains in the dark energy figure-of-merit (FoM) from combining magnification with shear for different scenarios regarding systematics: accounting for intrinsic alignments but no systematics for magnification, including magnification could improve the FoM by up to a factor of ∼2.5, whilst when accounting for physical systematics in both shear and magnification we anticipate a gain between ∼25 and ∼65 per cent. The fact that shear and magnification are subject to different systematics makes magnification an attractive complement to any cosmic shear analysis.
Kitching TD, Heavens AF, Das S, 2015, 3D weak gravitational lensing of the CMB and galaxies, Monthly Notices of the Royal Astronomical Society, Vol: 449, Pages: 2205-2214, ISSN: 1365-2966
In this paper, we present a power spectrum formalism that combines the full 3D informationfrom the galaxy ellipticity field, with information from the cosmic microwave background(CMB). We include in this approach galaxy cosmic shear and galaxy intrinsic alignments,CMB deflection, CMB temperature, and CMB polarization data; including the interdatumpower spectra between all quantities. We apply this to forecasting cosmological parametererrors for CMB and imaging surveys and show that the additional covariance between theCMB and ellipticity measurements can improve dark energy equation of state measurementsby 30 per cent. We present predictions for Euclid-like, Planck, ACTPoL, and CoRE-like experimentsand show that the combination of cosmic shear and the CMB, from Euclid-like andCoRE-like experiments, could in principle measure the sum of neutrino masses with an errorof 0.003 eV, and the dark energy equation of state with an error on w0 of less than 0.02.
Heavens A, Jimenez R, Verde L, 2014, Standard Rulers, Candles, and Clocks from the Low-Redshift Universe, PHYSICAL REVIEW LETTERS, Vol: 113, ISSN: 0031-9007
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