Future Cosmic Shear Surveys Research Articles

Reconstructing the matter power spectrum with future cosmic shear surveys

ABSTRACT Analyses of cosmic shear typically condense weak lensing information over a range of scales to a single cosmological parameter, $S_8$. This paper presents a method to extract more information from Stage IV cosmic shear measurements by directly reconstructing the matter power spectrum from linear to non-linear scales. We demonstrate that cosmic shear surveys will be sensitive to the shape of the matter power spectrum on non-linear scales. We show that it should be possible to distinguish between different models of baryonic feedback and we investigate the impact of intrinsic alignments and observational systematics on forecasted constraints. In addition to providing important information on galaxy formation, power spectrum reconstruction should provide a definitive answer to the question of whether weak lensing measurements of $S_8$ on linear scales are consistent with the Planck Lambda cold dark matter cosmology. In addition, power spectrum reconstruction may lead to new discoveries on the composition of the dark sector.

Probing dark energy with tomographic weak-lensing aperture mass statistics

We forecast and optimize the cosmological power of various weak-lensing aperture mass (Map) map statistics for future cosmic shear surveys, including peaks, voids, and the full distribution of pixels (1DMap). These alternative methods probe the non-Gaussian regime of the matter distribution, adding complementary cosmological information to the classical two-point estimators. Based on the SLICS and cosmo-SLICSN-body simulations, we buildEuclid-like mocks to explore theS8 − Ωm − w0parameter space. We develop a new tomographic formalism that exploits the cross-information between redshift slices (cross-Map) in addition to the information from individual slices (auto-Map) probed in the standard approach. Our auto-Mapforecast precision is in good agreement with the recent literature on weak-lensing peak statistics and is improved by ∼50% when including cross-Map. It is further boosted by the use of 1DMapthat outperforms all other estimators, including the shear two-point correlation function (γ-2PCF). When considering all tomographic terms, our uncertainty range on the structure growth parameterS8is enhanced by ∼45% (almost twice better) when combining 1DMapand theγ-2PCF compared to theγ-2PCF alone. We additionally measure the first combined forecasts on the dark energy equation of statew0, finding a factor of three reduction in the statistical error compared to theγ-2PCF alone. This demonstrates that the complementary cosmological information explored by non-GaussianMapmap statistics not only offers the potential to improve the constraints on the recentσ8–Ωmtension, but also constitutes an avenue to understanding the accelerated expansion of our Universe.

KiDS+VIKING-450: Cosmic shear tomography with optical and infrared data

We present a tomographic cosmic shear analysis of the Kilo-Degree Survey (KiDS) combined with the VISTA Kilo-Degree Infrared Galaxy Survey. This is the first time that a full optical to near-infrared data set has been used for a wide-field cosmological weak lensing experiment. This unprecedented data, spanning 450 deg2, allows us to significantly improve the estimation of photometric redshifts, such that we are able to include robustly higher-redshift sources for the lensing measurement, and – most importantly – to solidify our knowledge of the redshift distributions of the sources. Based on a flat ΛCDM model we findS8≡ σ8Ωm/0.3 = 0.737+0.040−0.036in a blind analysis from cosmic shear alone. The tension between KiDS cosmic shear and the Planck-Legacy CMB measurements remains in this systematically more robust analysis, withS8differing by 2.3σ. This result is insensitive to changes in the priors on nuisance parameters for intrinsic alignment, baryon feedback, and neutrino mass. KiDS shear measurements are calibrated with a new, more realistic set of image simulations and no significant B-modes are detected in the survey, indicating that systematic errors are under control. When calibrating our redshift distributions by assuming the 30-band COSMOS-2015 photometric redshifts are correct (following the Dark Energy Survey and the Hyper Suprime-Cam Survey), we find the tension withPlanckis alleviated. The robust determination of source redshift distributions remains one of the most challenging aspects for future cosmic shear surveys.

Towards emulating cosmic shear data: revisiting the calibration of the shear measurements for the Kilo-Degree Survey

Exploiting the full statistical power of future cosmic shear surveys will necessitate improvements to the accuracy with which the gravitational lensing signal is measured. We present a framework for calibrating shear with image simulations that demonstrates the importance of including realistic correlations between galaxy morphology, size, and more importantly, photometric redshifts. This realism is essential to ensure that selection and shape measurement biases can be calibrated accurately for a tomographic cosmic shear analysis. We emulate Kilo-Degree Survey (KiDS) observations of the COSMOS field using morphological information fromHubbleSpace Telescope imaging, faithfully reproducing the measured galaxy properties from KiDS observations of the same field. We calibrate our shear measurements fromlensfit, and find through a range of sensitivity tests thatlensfit is robust and unbiased within the allowed two per cent tolerance of our study. Our results show that the calibration has to be performed by selecting the tomographic samples in the simulations, consistent with the actual cosmic shear analysis, because the joint distributions of galaxy properties are found to vary with redshift. Ignoring this redshift variation could result in misestimating the shear bias by an amount that exceeds the allowed tolerance. To improve the calibration for future cosmic shear analyses, it will also be essential to correctly account for the measurement of photometric redshifts, which requires simulating multi-band observations.

Effects of self-calibration of intrinsic alignment on cosmological parameter constraints from future cosmic shear surveys

Intrinsic alignments (IA) of galaxies have been recognized as one of the most serious contaminants to weak lensing. These systematics need to be isolated and mitigated in order for ongoing and future lensing surveys to reach their full potential. The IA self-calibration (SC) method was shown in previous studies to be able to reduce the GI contamination by up to a factor of 10 for the 2-point and 3-point correlations. The SC method does not require the assumption of an IA model in its working and can extract the GI signal from the same photo-z survey offering the possibility to test and understand structure formation scenarios and their relationship to IA models. In this paper, we study the effects of the IA SC mitigation method on the precision and accuracy of cosmological parameter constraints from future cosmic shear surveys LSST, WFIRST and Euclid. We perform analytical and numerical calculations to estimate the loss of precision and the residual bias in the best fit cosmological parameters after the self-calibration is performed. We take into account uncertainties from photometric redshifts and the galaxy bias. We find that the confidence contours are slightly inflated from applying the SC method itself while a significant increase is due to the inclusion of the photo-z uncertainties. The bias of cosmological parameters is reduced from several-σ, when IA is not corrected for, to below 1-σ after SC is applied. These numbers are comparable to those resulting from applying the method of marginalizing over IA model parameters despite the fact that the two methods operate very differently. We conclude that implementing the SC for these future cosmic-shear surveys will not only allow one to efficiently mitigate the GI contaminant but also help to understand their modeling and link to structure formation.

Cross-correlation cosmic shear with the SDSS and VLA FIRST surveys

We measure the cosmic shear power spectrum on large angular scales by cross-correlating the shapes of ~9 million galaxies measured in the optical SDSS survey with the shapes of ~2.7x10^5 radio galaxies measured by the overlapping VLA-FIRST survey. Our measurements span the multipole range 10 < l < 130, corresponding to angular scales 2deg < {\theta} < 20deg. On these scales, the shear maps from both surveys suffer from significant systematic effects that prohibit a measurement of the shear power spectrum from either survey alone. Conversely we demonstrate that a power spectrum measured by cross-correlating the two surveys is unbiased. We measure an E-mode power spectrum from the data that is inconsistent with zero signal at the 99\% confidence (~2.7{\sigma}) level. The odd-parity B-mode signal and the EB cross- correlation are both found to be consistent with zero (within 1{\sigma}). These constraints are obtained after a careful error analysis that accounts for uncertainties due to cosmic variance, random galaxy shape noise and shape measurement errors, as well as additional errors associated with the observed large-scale systematic effects in the two surveys. Our constraints are consistent with the expected signal in the concordance cosmological model assuming recent estimates of the cosmological parameters from the Planck satellite, and literature values for the median redshifts of the SDSS and FIRST galaxy populations. The cross-power spectrum approach described in this paper represents a powerful technique for mitigating shear systematics and will be ideal for extracting robust results, with the exquisite control of systematics required, from future cosmic shear surveys with the SKA, LSST, Euclid and WFIRST-AFTA.

The impact of intrinsic alignment on current and future cosmic shear surveys

Intrinsic alignment (IA) of source galaxies is one of the major astrophysical systematics for ongoing and future weak lensing surveys. This paper presents the first forecasts of the impact of IA on cosmic shear measurements for current and future surveys (DES, Euclid, LSST, WFIRST) using simulated likelihood analyses and realistic covariances that include higher-order moments of the density field in the computation. We consider a range of possible IA scenarios and test mitigation schemes, which parameterize IA by the fraction of red galaxies, normalization, luminosity and redshift dependence of the IA signal (for a subset we consider joint IA and photo-z uncertainties). Compared to previous studies we find smaller biases in time-dependent dark energy models if IA is ignored in the analysis; the amplitude and significance of these biases vary as a function of survey properties (depth, statistical uncertainties), luminosity function, and IA scenario: Due to its small statistical errors and relatively shallow observing strategy Euclid is significantly impacted by IA. LSST and WFIRST benefit from their increased survey depth, while the larger statistical errors for DES decrease IA's relative impact on cosmological parameters. The proposed IA mitigation scheme removes parameter biases due to IA for DES, LSST, and WFIRST even if the shape of the IA power spectrum is only poorly known; successful IA mitigation for Euclid requires more prior information. We explore several alternative IA mitigation strategies for Euclid; in the absence of alignment of blue galaxies we recommend the exclusion of red (IA contaminated) galaxies in cosmic shear analyses. We find that even a reduction of 20% in the number density of galaxies only leads to a 4-10% loss in cosmological constraining power.

Constraining primordial magnetic fields with future cosmic shear surveys

The origin of astrophysical magnetic fields observed in galaxies and clusters of galaxies is still unclear. One possibility is that primordial magnetic fields generated in the early Universe provide seeds that grow through compression and turbulence during structure formation. A cosmological magnetic field present prior to recombination would produce substantial matter clustering at intermediate/small scales, on top of the standard inflationary power spectrum. In this work we study the effect of this alteration on one particular cosmological observable, cosmic shear. We adopt the semi-analytic halo model in order to describe the non-linear clustering of matter, and feed it with the altered mass variance induced by primordial magnetic fields. We find that the convergence power spectrum is, as expected, substantially enhanced at intermediate/small angular scales, with the exact amplitude of the enhancement depending on the magnitude and power-law index of the magnetic field power spectrum. Specifically, for a fixed amplitude, the effect of magnetic fields is larger for larger spectral indices. We use the predicted statistical errors for a future wide-field cosmic shear survey, on the model of the ESA Cosmic Vision mission Euclid, in order to forecast constraints on the amplitude of primordial magnetic fields as a function of the spectral index. We find that the amplitude will be constrained at the level of ∼ 0.1 nG for nB ∼ −3, and at the level of ∼ 10−7 nG for nB ∼ 3. The latter is at the same level of lower bounds coming from the secondary emission of gamma-ray sources, implying that for high spectral indices Euclid will certainly be able to detect primordial magnetic fields, if they exist. The present study shows how large-scale structure surveys can be used for both understanding the origins of astrophysical magnetic fields and shedding new light on the physics of the pre-recombination Universe.

The impact of galaxy colour gradients on cosmic shear measurement

Cosmic shear has been identified as the method with the most potential to constrain dark energy. To capitalise on this potential it is necessary to measure galaxy shapes with great accuracy, which in turn requires a detailed model for the image blurring, the Point Spread Function (PSF). In general the PSF varies with wavelength and therefore the PSF integrated over an observing filter depends on the spectrum of the object. For a typical galaxy the spectrum varies across the galaxy image, thus the PSF depends on the position within the image. We estimate the bias on the shear due to such colour gradients by modelling galaxies using two co-centered, co-elliptical Sersic profiles, each with a different spectrum. We estimate the effect of ignoring colour gradients and find the shear bias from a single galaxy can be very large depending on the properties of the galaxy. We find that halving the filter width reduces the shear bias by a factor of about 5. We show that, to first order, tomographic cosmic shear two point statistics depend on the mean shear bias over the galaxy population at a given redshift. For a single broad filter, and averaging over a small galaxy catalogue, we find a mean shear bias which is subdominant to the predicted statistical errors for future cosmic shear surveys. However, the true mean shear bias may exceed the statistical errors, depending on how accurately the catalogue represents the observed distribution of galaxies in the cosmic shear survey. We then investigate the bias on the shear for two-filter imaging and find that the bias is reduced by at least an order of magnitude. Lastly, we find that it is possible to calibrate galaxies for which colour gradients were ignored using two-filter imaging of a fair sample of noisy galaxies, if the galaxy model is known. For a S/N of 25 the number of galaxies required in each tomographic redshift bin is of order 1e4.

Shear and magnification: cosmic complementarity

The potential of cosmic shear to probe cosmology is well recognized and future optical wide field surveys are currently being designed to optimize the return of cosmic shear science. High precision cosmic shear analysis requires high precision photometric redshift. With accurate photometric redshifts, it becomes possible to measure the cosmic magnification on galaxies by galaxies and use it as a probe of cosmology. This type of weak lensing measurement will not use galaxy shapes, instead it will strongly rely on precise photometry and detailed color information. In this work it is shown that such a measurement would lead to competitive constraints of the cosmological parameters, with a remarkable complementarity with cosmic shear. Future cosmic shear surveys could gain tremendously from magnification measurements as an independent probe of the dark matter distribution leading to a better control of observational and theoretical systematics when combined with shear.

Optimal point spread function modeling for weak lensing: complexity and sparsity

We investigate the impact of point spread function (PSF) fitting errors on cosmic shear measurements using the concepts of complexity and sparsity. Complexity, introduced in a previous paper, characterizes the number of degrees of freedom of the PSF. For instance, fitting an underlying PSF with a model with low complexity will lead to small statistical errors on the model parameters, however these parameters could suffer from large biases. Alternatively, fitting with a large number of parameters will tend to reduce biases at the expense of statistical errors. We perform an optimisation of scatters and biases by studying the mean squared error of a PSF model. We also characterize a model sparsity, which describes how efficiently the model is able to represent the underlying PSF using a limited number of free parameters. We present the general case and illustrate it for a realistic example of PSF fitted with shapelet basis sets. We derive the relation between complexity and sparsity of the PSF model, signal-to-noise ratio of stars and systematic errors on cosmological parameters. With the constraint of maintaining the systematics below the statistical uncertainties, this lead to a relation between the required number of stars to calibrate the PSF and the sparsity. We discuss the impact of our results for current and future cosmic shear surveys. In the typical case where the biases can be represented as a power law of the complexity, we show that current weak lensing surveys can calibrate the PSF with few stars, while future surveys will require hard constraints on the sparsity in order to calibrate the PSF with 50 stars.

Ray-tracing through the Millennium Simulation: Born corrections and lens-lens coupling in cosmic shear and galaxy-galaxy lensing

(abridged) We study the accuracy of various approximations to cosmic shear and weak galaxy-galaxy lensing and investigate effects of Born corrections and lens-lens coupling. We use ray-tracing through the Millennium Simulation to calculate various cosmic-shear and galaxy-galaxy-lensing statistics. We compare the results from ray-tracing to semi-analytic predictions. We find: (i) The linear approximation provides an excellent fit to cosmic-shear power spectra as long as the actual matter power spectrum is used as input. Common fitting formulae, however, strongly underestimate the cosmic-shear power spectra. Halo models provide a better fit to cosmic shear-power spectra, but there are still noticeable deviations. (ii) Cosmic-shear B-modes induced by Born corrections and lens-lens coupling are at least three orders of magnitude smaller than cosmic-shear E-modes. Semi-analytic extensions to the linear approximation predict the right order of magnitude for the B-mode. Compared to the ray-tracing results, however, the semi-analytic predictions may differ by a factor two on small scales and also show a different scale dependence. (iii) The linear approximation may under- or overestimate the galaxy-galaxy-lensing shear signal by several percent due to the neglect of magnification bias, which may lead to a correlation between the shear and the observed number density of lenses. We conclude: (i) Current semi-analytic models need to be improved in order to match the degree of statistical accuracy expected for future weak-lensing surveys. (ii) Shear B-modes induced by corrections to the linear approximation are not important for future cosmic-shear surveys. (iii) Magnification bias can be important for galaxy-galaxy-lensing surveys.

Intrinsic galaxy alignments from the 2SLAQ and SDSS surveys: luminosity and redshift scalings and implications for weak lensing surveys

Correlations between intrinsic shear and the density field on large scales, a potentially important contaminant for cosmic shear surveys, have been robustly detected at low redshifts with bright galaxies in Sloan Digital Sky Survey (SDSS) data. Here we present a more detailed characterization of this effect, which can cause anticorrelations between gravitational lensing shear and intrinsic ellipticity (GI correlations). This measurement uses 36 278 luminous red galaxies (LRGs) from the SDSS spectroscopic sample with 0.15 3σ detections of the effect on large scales (up to 60 h−1 Mpc) for all galaxy subsamples within the SDSS LRG sample; for the 2SLAQ sample, we find a 2σ detection for a bright subsample, and no detection for a fainter subsample. Fitting formulae are provided for the scaling of the GI correlations with luminosity, transverse separation and redshift (for which the 2SLAQ sample, while small, provides crucial constraints due to its longer baseline in redshift). We estimate contamination in the measurement of σ8 for future cosmic shear surveys on the basis of the fitted dependence of GI correlations on galaxy properties. We find contamination to the power spectrum ranging from −1.5 per cent (optimistic) to −33 per cent (pessimistic) for a toy cosmic shear survey using all galaxies to a depth of R = 24 using scales l ≈ 500, though the central value of predicted contamination is −6.5 per cent. This corresponds to a bias in σ8 of Δσ8 = −0.004 (optimistic), −0.02 (central) or −0.10 (pessimistic). We provide a prescription for inclusion of this error in cosmological parameter estimation codes. The principal uncertainty is in the treatment of the L ≤ L blue galaxies, for which we have no detection of the GI signal, but which could dominate the GI contamination if their GI amplitude is near our upper limits. Characterization of the tidal alignments of these galaxies, especially at redshifts relevant for cosmic shear, should be a high priority for the cosmic shear community.

The ring statistics – how to separate E- and B-modes of cosmic shear correlation functions on a finite interval

Aims. One of the main probes for systematic errors in the cosmic shear signal are the division of the shear field into E- and B-mode shear, where gravitational lensing only produces the former. As shown in a recent note, all currently used E-/B-mode separation methods for the shear correlation functions xi_pm require them to be measured to arbitrarily small and/or large separations which is of course not feasible in practice. Methods. We derive second-order shear statistics which provide a clean separation into E- and B-modes from measurements of xi_pm(theta) over a finite interval only. We call these new statistics the circle and ring statistics, respectively; the latter is obtained by an integral over the former. The mathematical properties of these new shear statistics are obtained, as well as specific expressions for applying them to observed data. Results. It is shown that an E-/B-mode separation can be performed on measurements of xi_pm over a finite interval in angular separation, using the ring statistics. We furthermore generalize this result to derive the most general class of second-order shear statistics which provide a separation of E- and B-mode shear on a given angular interval theta_min <= theta <= theta_max. Our results will be of practical use particularly for future cosmic shear surveys where highly precise measurements of the shear will become available and where control of systematics will be mandatory.

Shapelets “Multiple Multipole” Shear Measurement

The measurement of weak gravitational lensing is currently limited to a precision of 10% by instabilities in galaxy shape measurement techniques and uncertainties in their calibration. The potential of large, on-going and future cosmic shear surveys will only be realised with the development of more accurate image analysis methods. We present a description of several possible shear measurement methods using the linear “shapelets” decomposition. Shapelets provides a complete reconstruction of any galaxy image, including higher-order shape moments that can be used to generalise the KSB method to arbitrary order. Many independent shear estimators can then be formed for each object, using linear combinations of shapelet coefficients. These estimators can be treated separately, to improve their overall calibration; or combined in more sophisticated ways, to eliminate various instabilities and a calibration bias. We apply several methods to simulated astronomical images containing a known input shear, and demonstrate the dramatic improvement in shear recovery using shapelets. A complete IDL software package to perform image analysis and manipulation in shapelet space can be downloaded from www.astro.caltech.edu/~rjm/shapelets/.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Power spectrum normalization and the non-Gaussian halo model

The normalization of the matter power spectrum, σ 8 , is an essential ingredient to predict the phenomenology of the low-redshift Universe. It has been measured using several methods, such as X-ray cluster counts, weak lensing and the cosmic microwave background (CMB), which have yielded values ranging from 0.7 to 1.0. While these differences could be due to systematic effects, they could also be due to physics beyond the standard A cold dark matter (ACDM) model. An obvious possibility is the presence of non-Gaussian initial fluctuations in the density field. To study the impact of non-Gaussianity on each of these methods, we use a generalized halo model to compute cluster counts and the non-linear power spectrum for non-Gaussian models. For the quadratic coupling model, the upper limits on non-Gaussianity from the WMAP CMB experiment correspond to roughly a 4 per cent shift in a 8 as measured from cluster counts and about 2 per cent shift through weak lensing. This is not enough to account for the current internal and mutual discrepancies between the different methods, unless the scale dependence of non-Gaussianity is stronger than that for quadratic coupling. A comparison between future X-ray surveys with a two-fold improvement in cluster mass calibration and future cosmic shear surveys with 400 deg 2 will be required to constrain non-Gaussianity on small scales with a precision matching that of the current CMB constraints on larger scales. Our results argue for the presence of systematics in the current cluster and cosmic shear surveys, or to non-standard physics other than non-Gaussianity.

Weak Gravitational Lensing by Large-Scale Structure

▪ Abstract Weak gravitational lensing provides a unique method to map directly the distribution of dark matter in the universe and to measure cosmological parameters. This cosmic-shear technique is based on the measurement of the weak distortions that lensing induces in the shape of background galaxies as photons travel through large-scale structures. This technique is now widely used to measure the mass distribution of galaxy clusters and has recently been detected in random regions of the sky. In this review, we present the theory and observational status of cosmic shear. We describe the principles of weak lensing and the predictions for the shear statistics in favored cosmological models. Next, we review the current measurements of cosmic shear and show how they constrain cosmological parameters. We then describe the prospects offered by upcoming and future cosmic-shear surveys as well as the technical challenges that have to be met for the promises of cosmic shear to be fully realized.