arXiv subjects

Alan F. Heavens

Publications and source records attributed to Alan F. Heavens.

At least 37 records · Page 2Linked to original sources

arXiv2017

Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference

We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the 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 2-bin tomographic analysis to constrain cosmological parameters and investigate the possibility of photometric redshift bias in the CFHTLenS data. Under the baseline $Λ$CDM model we constrain $S_8 = σ_8(Ω_\mathrm{m}/0.3)^{0.5} = 0.67 ^{\scriptscriptstyle+ 0.03 }_{\scriptscriptstyle- 0.03 }$ $(68\%)$, consistent with previous CFHTLenS analysis but in tension with Planck. Adding neutrino mass as a free parameter we are able to constrain $\sum m_ν< 4.6\mathrm{eV}$ (95%) using CFHTLenS data alone. Including a linear redshift dependent photo-$z$ bias $Δz = p_2(z - p_1)$, we find $p_1=-0.25 ^{\scriptscriptstyle+ 0.53 }_{\scriptscriptstyle- 0.60 }$ and $p_2 = -0.15 ^{\scriptscriptstyle+ 0.17 }_{\scriptscriptstyle- 0.15 }$, and tension with Planck is only alleviated under very conservative prior assumptions. Neither the non-minimal neutrino mass or photo-$z$ bias models are significantly preferred by the CFHTLenS (2-bin tomography) data.

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arXiv2017

The Limits of Cosmic Shear

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

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arXiv2017

Quantifying lost information due to covariance matrix estimation in parameter inference

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 a 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. We apply our results to DES Science Verification weak lensing data, detecting a 10% 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%, with an additional uncertainty of about 2%. Without any nuisance parameters 1900 simulations are sufficient to only lose 1% of information. We also derive an estimator for the Fisher matrix of the unknown true covariance matrix, two estimators of its inverse with different physical meanings, and an estimator for the optimally achievable figure of merit. The formalism here quantifies the gains to be made by running more simulated datasets, allowing decisions to be made about numbers of simulations in an informed way.

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arXiv2016

Early Cosmology Constrained

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 $Λ$CDM 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 $Ω_{\rm MR} < 0.006$ and extra radiation parameterised as extra effective neutrino species $2.3 < N_{\rm eff} < 3.2$ 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 $Λ$CDM 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 $r_{\rm s} = 147.4 \pm 0.7$ 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 $r_{\rm s} = 150 \pm 5$ Mpc.

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arXiv2016

The length of the low-redshift standard ruler

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 1A supernovæ (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 $Λ$CDM 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 CMB observations. However, in general, the two quantities need not coincide. We obtain constraints on the length of the low-redshift standard ruler: $r^h_{\rm s}=101.0 \pm 2.3 h^{-1}$ Mpc, when using only Type 1A supernovæ and Baryon acoustic oscillations, and $r_{\rm s}=150.0\pm 4.7 $ Mpc when using clocks to set the Hubble normalisation, while $r_{\rm s}=141.0\pm 5.5 $ Mpc when using the local Hubble constant determination (using both yields $r_{\rm s}=143.9\pm 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 {\em Planck} satellite, which assumes it is the sound horizon at the end of baryon drag.

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arXiv2016

Discrepancies between CFHTLenS cosmic shear & Planck: new physics or systematic effects?

There is currently a discrepancy in the measured value of the amplitude of matter clustering, parameterised using $σ_8$, inferred from galaxy weak lensing, and cosmic microwave background 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 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 fit 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. (2015), based on spectroscopic redshifts; and that these conclusions are robust to assumptions about the intrinsic alignment systematic. We also find an upper limit on the sum of neutrino masses conditional on other $Λ$CDM parameters being fixed, of $< 0.28$ eV ($1σ$).

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arXiv2016

Cluster mass profile reconstruction with size and flux magnification on the HST STAGES survey

We present the first measurement of individual cluster mass estimates using weak lensing size and flux magnification. Using data from the HST-STAGES 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% 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 $0.77 \pm 0.18$ lower than the shear measurements.

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arXiv2016

Parameter inference with estimated covariance matrices

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 marginalising 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, marginalisation 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.

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arXiv2013

Clipping the Cosmos II: Cosmological information from non-linear scales

We present a method for suppressing contributions from higher-order terms in perturbation theory, greatly increasing the amount of information which may be extracted from the matter power spectrum. In an evolved cosmological density field the highest density regions are responsible for the bulk of the nonlinear power. By suitably down-weighting these problematic regions we find that the one- and two-loop terms are typically reduced in amplitude by ~70 per cent and ~95 per cent respectively, relative to the linear power spectrum. This greatly facilitates modelling the shape of the galaxy power spectrum, potentially increasing the number of useful Fourier modes by more than two orders of magnitude. We provide a demonstration of how this technique allows the galaxy bias and the amplitude of linear matter perturbations sigma_8 to be determined from the power spectrum on conventionally nonlinear scales, 0.1<k<0.7 h/Mpc.

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arXiv2013

Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7σ for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.

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arXiv2013

Size magnification as a complement to Cosmic Shear

We investigate the extent to which cosmic size magnification may be used to com- plement cosmic shear in weak gravitational lensing surveys, with a view to obtaining high-precision estimates of cosmological parameters. Using simulated galaxy images, we find that size estimation can be an excellent complement, finding that unbiased estimation of the convergence field is possible with galaxies with angular sizes larger than the point-spread function (PSF) and signal-to-noise ratio in excess of 10. The statistical power is similar to, but not quite as good as, cosmic shear, and it is subject to different systematic effects. Application to ground-based data will be challeng- ing, with relatively large empirical corrections required to account for with biases for galaxies which are smaller than the PSF, but for space-based data with 0.1 arcsecond resolution, the size distribution of galaxies brighter than i=24 is ideal for accurate estimation of cosmic size magnification.

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arXiv2011

Clipping the Cosmos: The Bias and Bispectrum of Large Scale Structure

A large fraction of the information collected by cosmological surveys is simply discarded to avoid lengthscales which are difficult to model theoretically. We introduce a new technique which enables the extraction of useful information from the bispectrum of galaxies well beyond the conventional limits of perturbation theory. Our results strongly suggest that this method increases the range of scales where the relation between the bispectrum and power spectrum in tree-level perturbation theory may be applied, from k_max ~ 0.1 h/Mpc to ~ 0.7 h/Mpc. This leads to correspondingly large improvements in the determination of galaxy bias. Since the clipped matter power spectrum closely follows the linear power spectrum, there is the potential to use this technique to probe the growth rate of linear perturbations and confront theories of modified gravity with observation.

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arXiv2011

Testing homogeneity with the fossil record of galaxies

The standard Friedmann model of cosmology is based on the Copernican Principle, i.e. the assumption of a homogeneous background on which structure forms via perturbations. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we interpret observations of the CMB and the galaxy distribution. It is therefore important to probe homogeneity via observations. We describe a test based on the fossil record of distant galaxies: if we can reconstruct key intrinsic properties of galaxies as functions of proper time along their worldlines, we can compare such properties at the same proper time for our galaxy and others. We achieve this by computing the lookback time using radial Baryon Acoustic Oscillations, and the time along galaxy world line using stellar physics, allowing us to probe homogeneity, in principle anywhere inside the past light cone. Agreement in the results would be an important consistency test -- although it would not in itself prove homogeneity. Any significant deviation in the results however would signal a breakdown of homogeneity.

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arXiv2011

Cosmic magnification: nulling the intrinsic clustering signal

We investigate the extent to which the pure magnification effect of gravitational lensing can be extracted from galaxy clustering statistics, by a nulling method which aims to eliminate terms arising from the intrinsic clustering of galaxies. The aim is to leave statistics which are free from the uncertainties of galaxy bias. We find that nulling can be done effectively, leaving data which are relatively insensitive to uncertainties in galaxy bias and its evolution, leading to cosmological parameter estimation which is effectively unbiased. This advantage comes at the expense of increased statistical errors, which are in some cases large, but it offers a robust alternative analysis method to cosmic shear for cosmological imaging surveys designed for weak lensing studies, or to full modelling of the clustering signal including magnification effects.

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arXiv2011

Measuring Unified Dark Matter with 3D Cosmic Shear

We present parameter estimation forecasts for future 3D cosmic shear surveys for a class of Unified Dark Matter (UDM) models, where a single scalar field mimics both Dark Matter (DM) and Dark Energy (DE). These models have the advantage that they can describe the dynamics of the Universe with a single matter component providing an explanation for structure formation and cosmic acceleration. A crucial feature of the class of UDM models we use in this work is characterised by a parameter, c_inf (in units of the speed of light c=1), that is the value of the sound speed at late times, and on which structure formation depends. We demonstrate that the properties of the DM-like behaviour of the scalar field can be estimated with very high precision with large-scale, fully 3D weak lensing surveys. We found that 3D weak lensing significantly constrains c_inf, and we find minimal errors 0.00003, for the fiducial value c_inf=0.001, and 0.000026, for c_inf=0.012. Moreover, we compute the Bayesian evidence for UDM models over the LCDM model as a function of c_inf. For this purpose, we can consider the LCDM model as a UDM model with c_inf=0. We find that the expected evidence clearly shows that the survey data would unquestionably favour UDM models over the LCDM model, for the values c_inf>0.001.

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arXiv2010

The stellar evolution of Luminous Red Galaxies, and its dependence on colour, redshift, luminosity and modelling

We present a series of colour evolution models for Luminous Red Galaxies (LRGs) in the 7th spectroscopic data release of the Sloan Digital Sky Survey (SDSS), computed using the full-spectrum fitting code VESPA on high signal-to-noise stacked spectra. The colour-evolution models are computed as a function of colour, luminosity and redshift, and we do not a-priori assume that LRGs constitute a uniform population of galaxies in terms of stellar evolution. By computing star-formation histories from the fossil record, the measured stellar evolution of the galaxies is decoupled from the survey's selection function, which also evolves with redshift. We present these evolutionary models computed using three different sets of Stellar Population Synthesis (SPS) codes. We show that the traditional fiducial model of purely passive stellar evolution of LRGs is broadly correct, but it is not sufficient to explain the full spectral signature. We also find that higher-order corrections to this model are dependent on the SPS used, particularly when calculating the amount of recent star formation. The amount of young stars can be non-negligible in some cases, and has important implications for the interpretation of the number density of LRGs within the selection box as a function of redshift. Dust extinction, however, is more robust to the SPS modelling: extinction increases with decreasing luminosity, increasing redshift, and increasing r-i colour. We are making the colour evolution tracks publicly available at http://www.icg.port.ac.uk/~tojeiror/lrg_evolution/.

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arXiv2009

On lensing by a cosmological constant

Several recent papers have suggested that the cosmological constant Lambda directly influences the gravitational deflection of light. We place this problem in a cosmological context, deriving an expression for the linear potentials which control the cosmological bending of light, finding that it has no explicit dependence on the cosmological constant. To explore the physical origins of the apparent Lambda-dependent potential that appears in the static Kottler metric, we highlight the two classical effects which lead to the aberration of light. The first relates to the observer's motion relative to the source, and encapsulates the familiar concept of angular-diameter distance. The second term, which has proved to be the source of debate, arises from cosmic acceleration, but is rarely considered since it vanishes for photons with radial motion. This apparent form of light-bending gives the appearance of curved geodesics even within a flat and homogeneous universe. However this cannot be construed as a real lensing effect, since its value depends on the observer's frame of reference. Our conclusion is thus that standard results for gravitational lensing in a universe containing Lambda do not require modification, with any influence of Lambda being restricted to negligible high-order terms.

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arXiv2009

A public catalogue of stellar masses, star formation and metallicity histories and dust content from the Sloan Digital Sky Survey using VESPA

We applied the VESPA algorithm to the Sloan Digital Sky Survey final data release of the Main Galaxies and Luminous Red Galaxies samples. The result is a catalogue of stellar masses, detailed star formation and metallicity histories and dust content of nearly 800,000 galaxies. We make the catalogue public via a T-SQL database, which is described in detail in this paper. We present the results using a range of stellar population and dust models, and will continue to update the catalogue as new and improved models are made public. The data and documentation are currently online, and can be found at http://www-wfau.roe.ac.uk/vespa/. We also present a brief exploration of the catalogue, and show that the quantities derived are robust: luminous red galaxies can be described by one to three populations, whereas a main galaxy sample galaxy needs on average two to five; red galaxies are older and less dusty; the dust values we recover are well correlated with measured Balmer decrements and star formation rates are also in agreement with previous measurements.

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