arXiv subjects

Alan Heavens

Publications and source records attributed to Alan Heavens.

At least 73 records · Page 4Linked to original sources

arXiv2010

The Ages of Type Ia Supernova Progenitors

Using light curves and host galaxy spectra of 101 Type Ia supernovae (SNe Ia) with redshift $z \lesssim 0.3$ from the SDSS Supernova Survey (SDSS-SN), we derive the SN Ia rate as a function of progenitor age (the delay time distribution, or DTD). We use the VESPA stellar population synthesis algorithm to analyze the SDSS spectra of all galaxies in the field searched by SDSS-SN, giving us a reference sample of 77,000 galaxies for our SN Ia hosts. Our method does not assume any a priori shape for the DTD and therefore is minimally parametric. We present the DTD in physical units for high stretch (luminous, slow declining) and low stretch (subluminous, fast declining) supernovae in three progenitor age bins. We find strong evidence of two progenitor channels: one that produces high stretch SNe Ia $\lesssim 400$ Myr after the birth of the progenitor system, and one that produces low stretch SNe Ia with a delay $\gtrsim 2.4$ Gyr. We find that each channel contributes roughly half of the Type Ia rate in our reference sample. We also construct the average spectra of high stretch and low stretch SN Ia host galaxies, and find that the difference of these spectra looks like a main sequence B star with nebular emission lines indicative of star formation. This supports our finding that there are two populations of SNe Ia, and indicates that the progenitors of high stretch SNe are at the least associated with very recent star formation in the last few tens of Myr. Our results provide valuable constraints for models of Type Ia progenitors and may help improve the calibration of SNe Ia as standard candles.

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arXiv2010

CMB Constraints on Primordial non-Gaussianity from the Bispectrum (f_{NL}) and Trispectrum (g_{NL} and τ_{NL}) and a New Consistency Test of Single-Field Inflation

We outline the expected constraints on non-Gaussianity from the cosmic microwave background (CMB) with current and future experiments, focusing on both the third (f_{NL}) and fourth-order (g_{NL} and τ_{NL}) amplitudes of the local configuration or non-Gaussianity. The experimental focus is the skewness (two-to-one) and kurtosis (two-to-two and three-to-one) power spectra from weighted maps. In adition to a measurement of τ_{NL} and g_{NL} with WMAP 5-year data, our study provides the first forecasts for future constraints on g_{NL}. We describe how these statistics can be corrected for the mask and cut-sky through a window function, bypassing the need to compute linear terms that were introduced for the previous-generation non-Gaussianity statistics, such as the skewness estimator. We discus the ratio A_{NL} = τ_{NL}/(6f_{NL}/5)^2 as an additional test of single-field inflationary models and discuss the physical significance of each statistic. Using these estimators with WMAP 5-Year V+W-band data out to l_{max}=600 we constrain the cubic order non-Gaussianity parameters τ_{NL}, and g_{NL} and find -7.4 < g_{NL}/10^5 < 8.2 and -0.6 < τ_{NL}/10^4 < 3.3 improving the previous COBE-based limit on τ_{NL} < 10^8 nearly four orders of magnitude with WMAP.

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arXiv2010

Statistical techniques in cosmology

In these lectures I cover a number of topics in cosmological data analysis. I concentrate on general techniques which are common in cosmology, or techniques which have been developed in a cosmological context. In fact they have very general applicability, for problems in which the data are interpreted in the context of a theoretical model, and thus lend themselves to a Bayesian treatment. We consider the general problem of estimating parameters from data, and consider how one can use Fisher matrices to analyse survey designs before any data are taken, to see whether the survey will actually do what is required. We outline numerical methods for estimating parameters from data, including Monte Carlo Markov Chains and the Hamiltonian Monte Carlo method. We also look at Model Selection, which covers various scenarios such as whether an extra parameter is preferred by the data, or answering wider questions such as which theoretical framework is favoured, using General Relativity and braneworld gravity as an example. These notes are not a literature review, so there are relatively few references.

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arXiv2010

A Measurement of Cubic-Order Primordial Non-Gaussianity (g_{NL} and τ_{NL}) With WMAP 5-Year Data

We measure two higher-order power spectra involving weighted cubic and squared temperature anisotropy maps from WMAP 5-year data to study the trispectrum generated by primordial non-Gaussianity. Using these measurements combined with Gaussian and noise simulations, we constrain the cubic order non-Gaussianity parameters τ_{NL}, and g_{NL}. With V+W-band data out to l_{max}=600, we find -7.4 < g_{\rm NL}/10^5 < 8.2 and -0.6 < τ_{\rm NL}/10^4 < 3.3 improving the previous COBE-based limit on τ_{\rm NL} < 10^8 nearly four orders of magnitude with WMAP. We find that the ratio of trispectrum to bispectrum amplitude as captured by the ratio of τ_{\rm Nl}/(6f_{\rm NL}/5)^2 ranges from -3 to 21 at the 95% confidence level.

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arXiv2010

Higher-order Statistics of Weak Lensing Shear and Flexion

Owing to their more extensive sky coverage and tighter control on systematic errors, future deep weak lensing surveys should provide a better statistical picture of the dark matter clustering beyond the level of the power spectrum. In this context, the study of non-Gaussianity induced by gravity can help tighten constraints on the background cosmology by breaking parameter degeneracies, as well as throwing light on the nature of dark matter, dark energy or alternative gravity theories. Analysis of the shear or flexion properties of such maps is more complicated than the simpler case of the convergence due to the spinorial nature of the fields involved. Here we develop analytical tools for the study of higher-order statistics such as the bispectrum (or trispectrum) directly using such maps at different source redshift. The statistics we introduce can be constructed from cumulants of the shear or flexions, involving the cross-correlation of squared and cubic maps at different redshifts. Typically, the low signal-to-noise ratio prevents recovery of the bispectrum or trispectrum mode by mode. We define power spectra associated with each multi- spectra which compresses some of the available information of higher order multispectra. We show how these can be recovered from a noisy observational data even in the presence of arbitrary mask, which introduces mixing between Electric (E-type) and Magnetic (B-type) polarization, in an unbiased way. We also introduce higher order cross-correlators which can cross-correlate lensing shear with different tracers of large scale structures.

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arXiv2010

Primordial Non-Gaussianity from a Joint Analysis of Cosmic Microwave Background Temperature and Polarization

We explore a systematic approach to the analysis of primordial non-Gaussianity using fluctuations in temperature and polarization of the Cosmic Microwave Background (CMB). Following Munshi & Heavens (2009), we define a set of power-spectra as compressed forms of the bispectrum and trispectrum derived from CMB temperature and polarization maps; these spectra compress the information content of the corresponding full multispectra and can be useful in constraining early Universe theories. We generalize the standard pseudo-C_l estimators in such a way that they apply to these spectra involving both spin-0 and spin-2 fields, developing explicit expressions which can be used in the practical implementation of these estimators. While these estimators are suboptimal, they are nevertheless unbiased and robust hence can provide useful diagnostic tests at a relatively small computational cost. We next consider approximate inverse-covariance weighting of the data and construct a set of near-optimal estimators based on that approach. Instead of combining all available information from the entire set of mixed bi- or trispectra, i.e multispectra describing both temperature and polarization information, we provide analytical constructions for individual estimators, associated with particular multispectra. The bias and scatter of these estimators can be computed using Monte-Carlo techniques. Finally, we provide estimators which are completely optimal for arbitrary scan strategies and involve inverse covariance weighting; we present the results of an error analysis performed using a Fisher-matrix formalism at both the one-point and two-point level.

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arXiv2010

Higher-order Convergence Statistics for Three-dimensional Weak Gravitational Lensing

Weak gravitational lensing on a cosmological scales can provide strong constraints both on the nature of dark matter and the dark energy equation of state. Most current weak lensing studies are restricted to (two-dimensional) projections, but tomographic studies with photometric redshifts have started, and future surveys offer the possibility of probing the evolution of structure with redshift. In future we will be able to probe the growth of structure in 3D and put tighter constraints on cosmological models than can be achieved by the use of galaxy redshift surveys alone. Earlier studies in this direction focused mainly on evolution of the 3D power spectrum, but extension to higher-order statistics can lift degeneracies as well as providing information on primordial non-gaussianity. We present analytical results for specific higher-order descriptors, the bispectrum and trispectrum, as well as collapsed multi-point statistics derived from them, i.e. cumulant correlators. We also compute quantities we call the power spectra associated with the bispectrum and trispectrum, the Fourier transforms of the well-known cumulant correlators. We compute the redshift dependence of these objects and study their performance in the presence of realistic noise and photometric redshift errors.

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arXiv2009

Weak lensing: Dark Matter, Dark Energy and Dark Gravity

In this non-specialist review I look at how weak lensing can provide information on the dark sector of the Universe. The review concentrates on what can be learned about Dark Matter, Dark Energy and Dark Gravity, and why. On Dark Matter, results on the confrontation of theoretical profiles with observation are reviewed, and measurements of neutrino masses discussed. On Dark Energy, the interest is whether this could be Einstein's cosmological constant, and prospects for high-precision studies of the equation of state are considered. On Dark Gravity, we consider the exciting prospects for future weak lensing surveys to distinguish General Relativity from extra-dimensional or other gravity theories.

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arXiv2009

New Optimised Estimators for the Primordial Trispectrum

Cosmic microwave background studies of non-Gaussianity involving higher-order multispectra can distinguish between early universe theories that predict nearly identical power spectra. However, the recovery of higher-order multispectra is difficult from realistic data due to their complex response to inhomogeneous noise and partial sky coverage, which are often difficult to model analytically. A traditional alternative is to use one-point cumulants of various orders, which collapse the information present in a multispectrum to one number. The disadvantage of such a radical compression of the data is a loss of information as to the source of the statistical behaviour. A recent study by Munshi & Heavens (2009) has shown how to define the skew spectrum (the power spectra of a certain cubic field, related to the bispectrum) in an optimal way and how to estimate it from realistic data. The skew spectrum retains some of the information from the full configuration-dependence of the bispectrum, and can contain all the information on non-Gaussianity. In the present study, we extend the results of the skew spectrum to the case of two degenerate power-spectra related to the trispectrum. We also explore the relationship of these power-spectra and cumulant correlators previously used to study non-Gaussianity in projected galaxy surveys or weak lensing surveys. We construct nearly optimal estimators for quick tests and generalise them to estimators which can handle realistic data with all their complexity in a completely optimal manner. We show how these higher-order statistics and the related power spectra are related to the Taylor expansion coefficients of the potential in inflation models, and demonstrate how the trispectrum can constrain both the quadratic and cubic terms.

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arXiv2009

Non-Gaussianity in WMAP Data Due to the Correlation of CMB Lensing Potential with Secondary Anisotropies

We measure the skewness power spectrum of the Cosmic Microwave Background (CMB) anisotropies optimized for a detection of the secondary bispectrum generated by the correlation of the CMB lensing potential with integrated Sachs-Wolfe effect and the Sunyaev-Zel'dovich effect. The covariance of our measurements is generated by Monte-Carlo simulations of Gaussian CMB fields with noise properties consistent with Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data. When interpreting multi-frequency measurements we also take into account the confusion resulting from unresolved radio point sources. We analyze Q, V and W-band WMAP 5-year raw and foreground-cleaned maps using the KQ75 mask out to l_max=600. We find no significant evidence for a non-zero non-Gaussian signal from the lensing-secondary correlation in all three bands and we constrain the overall amplitude of the cross power spectrum between CMB lensing potential and the sum of SZ and ISW fluctuations to be 0.42 \pm 0.86 and 1.19 \pm 0.86 in combined V and W-band raw and foreground-cleaned maps provided by the WMAP team, respectively. The point source amplitude at the bispectrum level measured with this skewness power spectrum is higher than previous measurements of point source non-Gaussianity. We also consider an analysis where we also account for the primordial non-Gaussianity in addition to lensing-secondary bispectrum and point sources. The focus of this paper is on secondary anisotropies. Consequently the estimator is not optimised for primordial non-Gaussianity and the limit we find on local non-Gaussianity from the foreground-cleaned V+W maps is f_NL = -13 \pm 62, when marginalized over point sources and lensing-ISW/SZ constributions to the total bispectrum.

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arXiv2009

Results of the GREAT08 Challenge: An image analysis competition for cosmological lensing

We present the results of the GREAT08 Challenge, a blind analysis challenge to infer weak gravitational lensing shear distortions from images. The primary goal was to stimulate new ideas by presenting the problem to researchers outside the shear measurement community. Six GREAT08 Team methods were presented at the launch of the Challenge and five additional groups submitted results during the 6 month competition. Participants analyzed 30 million simulated galaxies with a range in signal to noise ratio, point-spread function ellipticity, galaxy size, and galaxy type. The large quantity of simulations allowed shear measurement methods to be assessed at a level of accuracy suitable for currently planned future cosmic shear observations for the first time. Different methods perform well in different parts of simulation parameter space and come close to the target level of accuracy in several of these. A number of fresh ideas have emerged as a result of the Challenge including a re-examination of the process of combining information from different galaxies, which reduces the dependence on realistic galaxy modelling. The image simulations will become increasingly sophisticated in future GREAT challenges, meanwhile the GREAT08 simulations remain as a benchmark for additional developments in shear measurement algorithms.

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arXiv2009

Secondary non-Gaussianity and Cross-Correlation Analysis

We develop optimised estimators of two sorts of power spectra for fields defined on the sky, in the presence of partial sky coverage. The first is the cross-power spectrum of two fields on the sky; the second is the skew spectrum of three fields. These can probe the Integrated Sachs Wolfe Effect (ISW) at large angular scales and the Sunyaev Zéldovich (SZ) effect from hot gas in clusters at small angular scales. The skew spectrum, recently introduced by Munshi & Heavens (2009), is an optimised statistic which can be tuned to study a particular form of non-Gaussianity, such as may arise in the early Universe, but which retains information on the nature of non-Gaussianity. In this paper we develop the mathematical formalism for the skew spectrum of 3 different fields. When applied to the CMB, this allows us to explore the contamination of the skew spectrum by secondary sources of CMB fluctuations. Considering the three-point function, the study of the bispectrum provides valuable information regarding cross-correlation of secondaries with lensing of CMB with much higher significance compared to just the study involving CMB sky alone. We use our analytical models to study specific cases of cosmological interest which include cross-correlating CMB with various large scale tracers to probe ISW and SZ effects for cross spectral analysis and use the formalism to study the signal-to-noise ratio for detection of the weak lensing of the CMB by cross-correlating it with different tracers as well as point sources for CMB experiments such as Planck (abridged).

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arXiv2009

Determining the Neutrino Mass Hierarchy with Cosmology

The combination of current large scale structure and cosmic microwave background (CMB) anisotropies data can place strong constraints on the sum of the neutrino masses. Here we show that future cosmic shear experiments, in combination with CMB constraints, can provide the statistical accuracy required to answer questions about differences in the mass of individual neutrino species. Allowing for the possibility that masses are non-degenerate we combine Fisher matrix forecasts for a weak lensing survey like Euclid with those for the forthcoming Planck experiment. Under the assumption that neutrino mass splitting is described by a normal hierarchy we find that the combination Planck and Euclid will possibly reach enough sensitivity to put a constraint on the mass of a single species. Using a Bayesian evidence calculation we find that such future experiments could provide strong evidence for either a normal or an inverted neutrino hierachy. Finally we show that if a particular neutrino hierachy is assumed then this could bias cosmological parameter constraints, for example the dark energy equation of state parameter, by > 1σ, and the sum of masses by 2.3σ.

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arXiv2009

Adiabatic versus Isocurvature Non--Gaussianity

We study the extent to which one can distinguish primordial non--Gaussianity (NG) arising from adiabatic and isocurvature perturbations. We make a joint analysis of different NG models based on various inflationary scenarios: local-type and equilateral-type NG from adiabatic perturbations and local-type and quadratic-type NG from isocurvature perturbations together with a foreground contamination by point sources. We separate the Fisher information of the bispectrum of CMB temperature and polarization maps by l for the skew spectrum estimator introduced by Munshi & Heavens (2009) to study the scale dependence of the signal-to-noise ratio of different NG components and their correlations. We find that the adiabatic and the isocurvature modes are strongly correlated, though the phase difference of acoustic oscillations helps to distinguish them. The correlation between local-and equilateral-type is weak, but the two isocurvature modes are too strongly correlated to be discriminated. Point source contamination, to the extent to which it can be regarded as white noise, can be almost completely separated from the primordial components for l>100. Including correlations among the different components, we find that the errors of the NG parameters increase by 20-30% for the WMAP 5-year observation, but 5% for Planck observations.

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arXiv2009

Handbook for the GREAT08 Challenge: An image analysis competition for cosmological lensing

The GRavitational lEnsing Accuracy Testing 2008 (GREAT08) Challenge focuses on a problem that is of crucial importance for future observations in cosmology. The shapes of distant galaxies can be used to determine the properties of dark energy and the nature of gravity, because light from those galaxies is bent by gravity from the intervening dark matter. The observed galaxy images appear distorted, although only slightly, and their shapes must be precisely disentangled from the effects of pixelisation, convolution and noise. The worldwide gravitational lensing community has made significant progress in techniques to measure these distortions via the Shear TEsting Program (STEP). Via STEP, we have run challenges within our own community, and come to recognise that this particular image analysis problem is ideally matched to experts in statistical inference, inverse problems and computational learning. Thus, in order to continue the progress seen in recent years, we are seeking an infusion of new ideas from these communities. This document details the GREAT08 Challenge for potential participants. Please visit http://www.great08challenge.info for the latest information.

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arXiv2009

A New Approach to Probing Primordial Non-Gaussianity

We address the dual challenge of estimating deviations from Gaussianity arising in models of the Early Universe, whilst retaining information necessary to assess whether a detection of non-Gaussianity is primordial. We do this by constructing a new statistic, the bispectrum-related power spectrum, which is constructed from a map of the Cosmic Microwave Background. The estimator is optimised for primordial non-Gaussianity detection, but can also be useful in distinguishing primordial non-Gaussianity from secondary non-Gaussianity, such as may arise from unsubtracted point sources, or residuals from component separation. Extending earlier studies we present unbiased non-Gaussianity estimators optimised for partial sky coverage and inhomogeneous noise associated with realistic scan strategies, but which retain the ability to assess foreground contamination.

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arXiv2009

The Case for Deep, Wide-Field Cosmology

Much of the science case for the next generation of deep, wide-field optical/infrared surveys has been driven by the further study of dark energy. This is a laudable goal (and the subject of a companion white paper by Zhan et al.). However, one of the most important lessons of the current generation of surveys is that the interesting science questions at the end of the survey are quite different than they were when the surveys were being planned. The current surveys succeeded in this evolving terrain by being very general tools that could be applied to a number of very fundamental measurements. Likewise, the accessibility of the data enabled the broader cosmological and astronomical community to generate more science than the survey collaborations could alone. With that in mind, we should consider some of the basic physical and cosmological questions that surveys like LSST and JDEM-Wide will be able to address.

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arXiv2009

Exploring Dark Energy with Next-Generation Photometric Redshift Surveys

The coming decade will be an exciting period for dark energy research, during which astronomers will address the question of what drives the accelerated cosmic expansion as first revealed by type Ia supernova (SN) distances, and confirmed by later observations. The mystery of dark energy poses a challenge of such magnitude that, as stated by the Dark Energy Task Force (DETF), "nothing short of a revolution in our understanding of fundamental physics will be required to achieve a full understanding of the cosmic acceleration." The lack of multiple complementary precision observations is a major obstacle in developing lines of attack for dark energy theory. This lack is precisely what next-generation surveys will address via the powerful techniques of weak lensing (WL) and baryon acoustic oscillations (BAO) -- galaxy correlations more generally -- in addition to SNe, cluster counts, and other probes of geometry and growth of structure. Because of their unprecedented statistical power, these surveys demand an accurate understanding of the observables and tight control of systematics. This white paper highlights the opportunities, approaches, prospects, and challenges relevant to dark energy studies with wide-deep multiwavelength photometric redshift surveys. Quantitative predictions are presented for a 20000 sq. deg. ground-based 6-band (ugrizy) survey with 5-sigma depth of r~27.5, i.e., a Stage 4 survey as defined by the DETF.

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