Moment-Based Ellipticity Measurement as a Statistical Parameter Estimation Problem

We show that galaxy ellipticity estimation for weak gravitational lensing with unweighted image moments reduces to the problem of measuring a combination of the means of three independent normal random variables. Under very general assumptions, the intrinsic image moments of sources can be recovered from observations including effects such as the point-spread function and pixellation. Gaussian pixel noise turns these into three jointly normal random variables, the means of which are algebraically related to the ellipticity. We show that the random variables are approximately independent with known variances, and provide an algorithm for making them exactly independent. Once the framework is developed, we derive general properties of the ellipticity estimation problem, such as the signal-to-noise ratio, a generic form of an ellipticity estimator, and Cram\'er-Rao lower bounds for an unbiased estimator. We then derive the unbiased ellipticity estimator using unweighted image moments. We find that this unbiased estimator has a poorly behaved distribution and does not converge in practical applications, but demonstrates how to derive and understand the behaviour of new moment-based ellipticity estimators.Comment: 11 pages, 7 figures; v2 matches accepted version with minor change

Cosmology with photometric redshift surveys

We explore the utility of future photometric redshift imaging surveys for delineating the large-scale structure of the Universe, and assess the resulting constraints on the cosmological model. We perform two complementary types of analysis: (1) We quantify the statistical confidence and the accuracy with which such surveys will be able to detect and measure characteristic features in the clustering power spectrum such as the acoustic oscillations and the turnover, in a 'model-independent' fashion. We show for example that a 10,000 deg^2 imaging survey with depth r = 22.5 and photometric redshift accuracy dz/(1+z) = 0.03 will detect the acoustic oscillations with 99.9% confidence, measuring the associated preferred cosmological scale with 2% precision. Such a survey will also detect the turnover with 95% confidence, determining the corresponding scale with 20% accuracy. (2) By assuming a Lambda-CDM model power spectrum we calculate the confidence with which a non-zero baryon fraction can be deduced from such future galaxy surveys. We quantify 'wiggle detection' by calculating the number of standard deviations by which the baryon fraction is measured, after marginalizing over the shape parameter. This is typically a factor of four more significant (in terms of number of standard deviations) than the 'model-independent' result. We conclude that the precision with which the clustering pattern may be inferred from future photometric redshift surveys will be competitive with contemporaneous spectroscopic redshift surveys, assuming that systematic effects can be controlled. We also note that an analysis of Luminous Red Galaxies in the Sloan Digital Sky Survey may yield a marginal detection of acoustic oscillations in the imaging survey, in addition to that recently reported for the spectroscopic component.Comment: 23 pages, 22 figures, version accepted by MNRA

Cosmological baryonic and matter densities from 600,000 SDSS Luminous Red Galaxies with photometric redshifts

We analyze MegaZ-LRG, a photometric-redshift catalogue of Luminous Red Galaxies (LRGs) based on the imaging data of the Sloan Digital Sky Survey (SDSS) 4th Data Release. MegaZ-LRG, presented in a companion paper, contains 10^6 photometric redshifts derived with ANNz, an Artificial Neural Network method, constrained by a spectroscopic sub-sample of 13,000 galaxies obtained by the 2dF-SDSS LRG and Quasar (2SLAQ) survey. The catalogue spans the redshift range 0.4 < z < 0.7 with an r.m.s. redshift error ~ 0.03(1+z), covering 5,914 deg^2 to map out a total cosmic volume 2.5 h^-3 Gpc^3. In this study we use the most reliable 600,000 photometric redshifts to present the first cosmological parameter fits to galaxy angular power spectra from a photometric redshift survey. Combining the redshift slices with appropriate covariances, we determine best-fitting values for the matter and baryon densities of Omega_m h = 0.195 +/- 0.023 and Omega_b/Omega_m = 0.16 +/- 0.036 (with the Hubble parameter h = 0.75 and scalar index of primordial fluctuations n = 1 held fixed). These results are in agreement with and independent of the latest studies of the Cosmic Microwave Background radiation, and their precision is comparable to analyses of contemporary spectroscopic-redshift surveys. We perform an extensive series of tests which conclude that our power spectrum measurements are robust against potential systematic photometric errors in the catalogue. We conclude that photometric-redshift surveys are competitive with spectroscopic surveys for measuring cosmological parameters in the simplest vanilla models. Future deep imaging surveys have great potential for further improvement, provided that systematic errors can be controlled.Comment: 24 pages, 23 figures, MNRAS accepte

Cosmology with the Square Kilometre Array

We argue that the Square Kilometre Array has the potential to make both redshift (HI) surveys and radio continuum surveys that will revolutionize cosmological studies, provided that it has sufficient instantaneous field-of-view that these surveys can cover a hemisphere in a timescale ~1 yr. Adopting this assumption, we focus on two key experiments which will yield fundamental new measurements in cosmology, characterizing the properties of the mysterious dark energy which dominates the dynamics of today's Universe. Experiment I will map out ~10^9 HI galaxies to redshift z~1.5, providing the premier measurement of the clustering power spectrum of galaxies: accurately delineating the acoustic oscillations and the `turnover'. Experiment II will quantify the cosmic shear distortion of ~10^10 radio continuum sources, determining a precise power spectrum of the dark matter, and its growth as a function of cosmic epoch. We contrast the performance of the SKA in precision cosmology with that of other facilities which will, probably or possibly, be available on a similar timescale. We conclude that data from the SKA will yield transformational science as the direct result of four key features: (i) the immense cosmic volumes probed, exceeding future optical redshift surveys by more than an order of magnitude; (ii) well-controlled systematic effects such as the narrow `k-space window function' for Experiment I and the accurately-known `point-spread function' for Experiment II; (iii) the ability to measure with high precision large-scale modes in the clustering power spectra, for which nuisance effects such as non-linear structure growth, peculiar velocities and `galaxy bias' are minimised; and (iv) different degeneracies between key parameters to those which are inherent in the CMB.Comment: 20 pages, 8 figures. To appear in "Science with the Square Kilometer Array", eds. C.Carilli and S.Rawlings, New Astronomy Reviews (Elsevier: Amsterdam

Testing for a Super-Acceleration Phase of the Universe

We propose a method to probe the phenomenological nature of dark energy which makes no assumptions about the evolution of its energy density. We exemplify this method with a test for a super-acceleration phase of the universe i.e., a phase when the dark energy density grows as the universe expands. We show how such a phase can be detected by combining SNIa (SNAP-like) and CMB (Planck) data without making any assumptions about the evolution of the dark energy equation of state, or about the value of the matter density parameter.Comment: Matches version accepted for publication in PRD. Added discussion of the effect of the calibration parameter on detecting super-acceleration. 8 pages and 4 figure

Precision Cosmology? Not Just Yet

The recent announcement from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite experiment combined with other recent advances in observational cosmology verifies key components of the standard cosmological model. However, we argue that there remain some significant open issues regarding the basic history and composition of the Universe and uncertainties in some of the most important parameters.Comment: 2 pages, 2 figures. Online journal version http://www.sciencemag.org/cgi/content/full/299/5612/153

Cosmic Discordance: Are Planck CMB and CFHTLenS weak lensing measurements out of tune?

We examine the level of agreement between low redshift weak lensing data and the CMB using measurements from the CFHTLenS and Planck+WMAP polarization. We perform an independent analysis of the CFHTLenS six bin tomography results of Heymans et al. (2013). We extend their systematics treatment and find the cosmological constraints to be relatively robust to the choice of non-linear modeling, extension to the intrinsic alignment model and inclusion of baryons. We find that the 90% confidence contours of CFHTLenS and Planck+WP do not overlap even in the full 6-dimensional parameter space of $\Lambda$CDM, so the two datasets are discrepant. Allowing a massive active neutrino or tensor modes does not significantly resolve the disagreement in the full n-dimensional parameter space. Our results differ from some in the literature because we use the full tomographic information in the weak lensing data and marginalize over systematics. We note that adding a sterile neutrino to $\Lambda$CDM does bring the 8-dimensional 64% contours to overlap, mainly due to the extra effective number of neutrino species, which we find to be 0.84 $\pm$ 0.35 (68%) greater than standard on combining the datasets. We discuss why this is not a completely satisfactory resolution, leaving open the possibility of other new physics or observational systematics as contributing factors. We provide updated cosmology fitting functions for the CFHTLenS constraints and discuss the differences from ones used in the literature.Comment: 12 pages, 8 figures. We compare our findings with studies that include other low redshift probes of structure. An interactive figure is available at http://bit.ly/1oZH0KQ. This version is that accepted by MNRAS, and so includes changes based on the referee's comments, and updates to the analysis cod

The Redshift Sensitivities of Dark Energy Surveys

Great uncertainty surrounds dark energy, both in terms of its physics, and the choice of methods by which the problem should be addressed. Here we quantify the redshift sensitivities offered by different techniques. We focus on the three methods most adept at constraining w, namely supernovae, cosmic shear, and baryon oscillations. For each we provide insight into the family of w(z) models which are permitted for a particular constraint on either w=w0 or w=w0+wa(1-a). Our results are in the form of "weight functions", which describe the fitted model parameters as a weighted average over the true functional form. For example, we find the recent best-fit from the Supernovae Legacy Survey (w=-1.023) corresponds to the average value of w(z) over the range 0<z<0.4. Whilst there is a strong dependence on the choice of priors, each cosmological probe displays distinctive characteristics in their redshift sensitivities. In the case of proposed future surveys, a SNAP-like supernova survey probes a mean redshift of z ~ 0.3, with baryon oscillations and cosmic shear at z ~ 0.6. If we consider the evolution of w, sensitivities shift to slightly higher redshift. Finally, we find that the weight functions may be expressed as a weighted average of the popular "principal components".Comment: 11 pages, 10 figures, changes reflect published versio