Measuring Linear and Non-linear Galaxy Bias Using Counts-in-Cells in the Dark Energy Survey Science Verification Data

 

Authors: A. I. Salvador, F. J. Sánchez, A. Pagul et al.
Journal:  
Year: 07/2018
Download: ADS| Arxiv


Abstract

Non-linear bias measurements require a great level of control of potential systematic effects in galaxy redshift surveys. Our goal is to demonstrate the viability of using Counts-in-Cells (CiC), a statistical measure of the galaxy distribution, as a competitive method to determine linear and higher-order galaxy bias and assess clustering systematics. We measure the galaxy bias by comparing the first four moments of the galaxy density distribution with those of the dark matter distribution. We use data from the MICE simulation to evaluate the performance of this method, and subsequently perform measurements on the public Science Verification (SV) data from the Dark Energy Survey (DES). We find that the linear bias obtained with CiC is consistent with measurements of the bias performed using galaxy-galaxy clustering, galaxy-galaxy lensing, CMB lensing, and shear+clustering measurements. Furthermore, we compute the projected (2D) non-linear bias using the expansion $\delta_{g} = \sum_{k=0}^{3} (b_{k}/k!) \delta^{k}$, finding a non-zero value for $b_2$ at the $3\sigma$ level. We also check a non-local bias model and show that the linear bias measurements are robust to the addition of new parameters. We compare our 2D results to the 3D prediction and find compatibility in the large scale regime ($>30$ Mpc $h^{-1}$)

A highly precise shape-noise-free shear bias estimator

 

Authors: A. Pujol, M. Kilbinger, F. Sureau et al.
Journal:  
Year: 06/2018
Download: ADS| Arxiv


Abstract

We present a new method to estimate shear measurement bias in image simulations that significantly improves its precision with respect to the state-of-the-art methods. This method is based on measuring the shear response for individual images. We generate sheared versions of the same image to measure how the shape measurement changes with the changes in the shear, so that we obtain a shear response for each original image, as well as its additive bias. Using the exact same noise realizations for each sheared version allows us to obtain an exact estimation of its shear response. The estimated shear bias of a sample of galaxies comes from the measured averages of the shear response and individual additive bias. The precision of this method supposes an improvement with respect to previous methods since our method is not affected by shape noise. As a consequence, the method does not require shape noise cancellation for a precise estimation of shear bias. The method can be easily applied to many applications such as shear measurement validation and calibration, reducing the number of necessary simulated images by a few orders of magnitude to achieve the same precision requirements.

Breaking degeneracies in modified gravity with higher (than 2nd) order weak-lensing statistics

 

Authors: A. PeelV. Pettorino, C. Giocoli, J.-L. Starck, M. Baldi
Journal: A&A
Year: 2018
Download: ADS | arXiv


Abstract

General relativity (GR) has been well tested up to solar system scales, but it is much less certain that standard gravity remains an accurate description on the largest, that is, cosmological, scales. Many extensions to GR have been studied that are not yet ruled out by the data, including by that of the recent direct gravitational wave detections. Degeneracies among the standard model (ΛCDM) and modified gravity (MG) models, as well as among different MG parameters, must be addressed in order to best exploit information from current and future surveys and to unveil the nature of dark energy. We propose various higher-order statistics in the weak-lensing signal as a new set of observables able to break degeneracies between massive neutrinos and MG parameters. We have tested our methodology on so-called f(R) models, which constitute a class of viable models that can explain the accelerated universal expansion by a modification of the fundamental gravitational interaction. We have explored a range of these models that still fit current observations at the background and linear level, and we show using numerical simulations that certain models which include massive neutrinos are able to mimic ΛCDM in terms of the 3D power spectrum of matter density fluctuations. We find that depending on the redshift and angular scale of observation, non-Gaussian information accessed by higher-order weak-lensing statistics can be used to break the degeneracy between f(R) models and ΛCDM. In particular, peak counts computed in aperture mass maps outperform third- and fourth-order moments.

Testing (modified) gravity with 3D and tomographic cosmic shear

 

Authors: A. Spurio Mancini, R. Reischke, V. Pettorino, B.M. Scháefer, M. Zumalacárregui
Journal: Submitted to MNRAS
Year: 2018
Download: ADS | arXiv


Abstract

Cosmic shear, the weak gravitational lensing caused by the large-scale structure, is one of the primary probes to test gravity with current and future surveys. There are two main techniques to analyse a cosmic shear survey; a tomographic method, where correlations between the lensing signal in different redshift bins are used to recover redshift information, and a 3D approach, where the full redshift information is carried through the entire analysis. Here we compare the two methods, by forecasting cosmological constraints for future surveys like Euclid. We extend the 3D formalism for the first time to theories beyond the standard model, belonging to the Horndeski class. This includes the majority of universally coupled extensions to LCDM with one scalar degree of freedom in addition to the metric, which are still in agreement with current observations. Given a fixed background, the evolution of linear perturbations in Horndeski gravity is described by a set of four functions of time only. We model their time evolution assuming proportionality to the dark energy density fraction and place Fisher matrix constraints on the proportionality coefficients. We find that a 3D analysis can constrain Horndeski theories better than a tomographic one, in particular with a decrease in the errors on the Horndeski parameters of the order of 20 - 30%. This paper shows for the first time a quantitative comparison on an equal footing between Fisher matrix forecasts for both a fully 3D and a tomographic analysis of cosmic shear surveys. The increased sensitivity of the 3D formalism comes from its ability to retain information on the source redshifts along the entire analysis.


Summary

A new paper has been put on the arXiv, led by Alessio Spurio Mancini, PhD student of CosmoStat member Valeria Pettorino in collaboration with R. Reischke, B.M. Scháefer (Heidelberg) and M. Zumalacárregui (Berkeley LBNL and Paris Saclay IPhT).
The authors investigate the performance of a 3D analysis of cosmic shear measurements vs a tomographic analysis as a probe of Horndeski theories of modified gravity, setting constraints by means of a Fisher matrix analysis on the parameters that describe the evolution of linear perturbations, using the specifications of a future Euclid-like experiment. Constraints are shown on both the modified gravity parameters and on a set of standard cosmological parameters, including the sum of neutrino masses. The analysis is restricted to angular modes ell < 1000 and k < 1 h/Mpc to avoid the deeply non-linear regime of structure growth. Below the main results of the paper.

 
  • The signal-to-noise ratio of both a 3D analysis as well as a tomographic one is very similar.
  • 3D cosmic shear provides tighter constraints than tomography for most cosmological parameters, with both methods showing very similar degeneracies.
  • The gain of 3D vs tomography is particularly significant for the sum of the neutrino masses (factor 3). For the Horndeski parameters the
    gain is of the order of 20 - 30 % in the errors.
  •  In Horndeski theories, braiding and the effective Newton coupling parameters (\alpha_B and \alpha_M) are constrained better if the kineticity is higher.
  • We investigated the impact on non-linear scales, and introduced an artificial screening scale, which pushes the deviations from General Relativity to zero below its value.  The gain when including the non-linear signal calls for the development of analytic or semi-analytic prescriptions for the treatment of non-linear scales in ΛCDM and modified gravity.

Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing

 

Authors: DES Collaboration
Journal:  
Year: 08/2017
Download: ADS| Arxiv


Abstract

We present cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing, using 1321 deg$^2$ of $griz$ imaging data from the first year of the Dark Energy Survey (DES Y1). We combine three two-point functions: (i) the cosmic shear correlation function of 26 million source galaxies in four redshift bins, (ii) the galaxy angular autocorrelation function of 650,000 luminous red galaxies in five redshift bins, and (iii) the galaxy-shear cross-correlation of luminous red galaxy positions and source galaxy shears. To demonstrate the robustness of these results, we use independent pairs of galaxy shape, photometric redshift estimation and validation, and likelihood analysis pipelines. To prevent confirmation bias, the bulk of the analysis was carried out while blind to the true results; we describe an extensive suite of systematics checks performed and passed during this blinded phase. The data are modeled in flat $\Lambda$CDM and $w$CDM cosmologies, marginalizing over 20 nuisance parameters, varying 6 (for $\Lambda$CDM) or 7 (for $w$CDM) cosmological parameters including the neutrino mass density and including the 457 $\times$ 457 element analytic covariance matrix. We find consistent cosmological results from these three two-point functions, and from their combination obtain $S_8 \equiv \sigma_8 (\Omega_m/0.3)^{0.5} = 0.783^{+0.021}_{-0.025}$ and $\Omega_m = 0.264^{+0.032}_{-0.019}$ for $\Lambda$CDM for $w$CDM, we find $S_8 = 0.794^{+0.029}_{-0.027}$, $\Omega_m = 0.279^{+0.043}_{-0.022}$, and $w=-0.80^{+0.20}_{-0.22}$ at 68% CL. The precision of these DES Y1 results rivals that from the Planck cosmic microwave background measurements, allowing a comparison of structure in the very early and late Universe on equal terms. Although the DES Y1 best-fit values for $S_8$ and $\Omega_m$ are lower than the central values from Planck ...

Weak-lensing projections

Authors: M. Kilbinger, C. Heymans et al.
Journal: submitted to MNRAS
Year: 2017
Download: ADS | arXiv


Abstract

We compute the spherical-sky weak-lensing power spectrum of the shear and convergence. We discuss various approximations, such as flat-sky, and first- and second- order Limber equations for the projection. We find that the impact of adopting these approximations are negligible when constraining cosmological parameters from current weak lensing surveys. This is demonstrated using data from the Canada-France-Hawaii Lensing Survey (CFHTLenS). We find that the reported tension with Planck Cosmic Microwave Background (CMB) temperature anisotropy results cannot be alleviated, in contrast to the recent claim made by Kitching et al. (2016, version 1). For future large-scale surveys with unprecedented precision, we show that the spherical second-order Limber approximation will provide sufficient accuracy. In this case, the cosmic-shear power spectrum is shown to be in agreement with the full projection at the sub-percent level for l > 3, with the corresponding errors an order of magnitude below cosmic variance for all l. When computing the two-point shear correlation function, we show that the flat-sky fast Hankel transformation results in errors below two percent compared to the full spherical transformation. In the spirit of reproducible research, our numerical implementation of all approximations and the full projection are publicly available within the package nicaea at http://www.cosmostat.org/software/nicaea.


Summary

We discuss various methods to calculate projections for weak gravitational lensing: Since lenses galaxies pick up matter inhomogeneities of the cosmic web along the line of sight while photons from the galaxies propagate through the Universe to the observer, these inhomogeneities have to be projected to a 2D observable, the cumulative shear or convergence. The full projection involves three-dimensional integrals over highly oscillating Bessel functions, and can be time-consuming to compute numerically to high accuracy. Most previous work have therefore used approximations such as the Limber approximation, that reduce the integrals to 1D, and thereby neglecting modes along the line of sight.

The authors show that these projections are more than adequate for present surveys. Sub-percent accuracy is reached for l>20, for example as shown by the pink curve, which is the ratio of the case 'ExtL1Hyb' to the full projection. The abbreviation means 'extended', corresponding to the improved approximation introduced by LoVerde & Afshordi (2008), first-order Limber, and hybrid, since this is a hybrid between flat-sky and spherical coordinates. This case has been used in most of the recent publications (e.g. for KiDS), whereas the cast 'L1Fl' (first-order Limber flat-sky) was popular for most publications since 2014.

These approximations are sufficient for the small areas of current observations coming from CFHTLenS, KiDS, and DES, and well below cosmic variance of even future surveys (the figure shows Euclid - 15,000 deg2 and Kids -1,500 deg2).

K17_Fig1b

The paper then discusses the second-order Limber approximation, introduced in a general framework by LoVerde & Afshordi (2008), and applied to weak lensing in the current paper. The best 2nd-order case 'ExtL2Sph' reaches sub-percent accuracy down to l=3, sufficient for all future surveys.

The paper also computes the shear correlation function in real space, and shows that those approximations have a very minor influence.

We then go on to re-compute the cosmological constraints obtained in Kilbinger et al. (2013), and find virtually no change when choosing different approximations. Only the depreciated case 'ExtL1Fl' makes a noticeable difference, which is however still well within the statistical error bars. This case shows a particular slow convergence to the full projection.

Similar results have been derived in two other recent publications, Kitching et al. (2017), and Lemos, Challinor & Efstathiou (2017).
Note however that Kitching et al. (2017) conclude that errors from projection approximations of the types we discussed here (Limber, flat sky) could make up to 11% of the error budget of future surveys. This is however assuming the worst-case scenario including the deprecated cast 'ExtL1Fl', and we do not share their conclusion, but think that for example the projection 'ExtL2Sph' is sufficient for future surveys such as LSST and Euclid.

The XXL Survey

First round of papers published

The XXL Survey is a deep X-ray survey observed with the XMM satellite, covering two fields of 25 deg2 each. Observations in many other wavelength, from radio to IR and optical, in both imaging and spectroscopy, complement the survey. The main science case is cosmology with X-ray selected galaxy clusters, but other fields such as galaxy evolution, AGNs, cluster physics, and the large-scale structure are being studied.

The main paper (Paper I) describing the survey and giving an overview of the science is arXiv:1512.04317 (Pierre et al. 2015). Paper IV (arxiv.org:1512.03857, Lieu et al. 2015) presents weak-lensing mass measurements of the brightest clusters in the Northern field, using CFHTLenS shapes and photometric redshifts.

 

The mass-temperature relation for XXL and other surveys (CCCP, COSMOS), Lieu et al (2015).

Review: Cosmology from cosmic shear observations

Martin Kilbinger, CEA Saclay, Service d'Astrophysique (SAp), France

Find on this page general information and updates for my recent review article (arXiv:1411.0155) on cosmic shear, Reports on Progress in Physics 78 (2015) 086901 (ads link for two-column format).

Sigma 12/17
Fig. 7 of the review article: The quantity \Sigma = \sigma_8 \left( \Omega_{\rm m}/0.3 \right)^\alpha as function of publication year.
 
 
 
Updated figure!
02/2015: Added Stripe-82 and CFHTLenS peak counts
07/2015: Added DES-SV.
06/2016: Added DLS, two more CFHTLenS analyses, DES-SV peak counts, and KiDS-450.
08/2017: Added DES-Y1, and another KiDS-450 result.
12/2017: Added more KiDS-450 and DES-Y1 results (peak counts, lensing+clustering, density-split statistic).
 
 
 
 

In the video abstract of the article I talk about cosmic shear and the review for a broader audience.
 
 
 
 
Additional references, new papers
General papers, new reviews.
 
    • Another weak-lensing review has been published by my colleagues Liping Fu and Zu-Hui Fan (behind a pay wall, not available on the arXiv).
    • Rachel Mandelbaum's short, pedagogical review to instrumental systematics and WL

 Sect. 2: Cosmological background

 Sect. 5: Measuring weak lensing

    • News on ensemble shape measurement methods:
      An implementation of the Bernstein &amp; Armstrong (2014) Bayesian shape method has been published at arXiv:1403.7669. The team that participated at the great3 challenge with the Bayesian inference method "MBI" published their pipeline and results paper, see arXiv:1411.2608.
    • Okura & Futamase (arXiv:1405.1539) came up with an estimator of ellipticity that uses 0th instead of 2nd-order moments!
    • arXiv:1409.6273 discusses atmospheric chromatic effects for LSST.
    • Dust in spiral galaxies  as source of shape bias, but also astrophysical probe: arXiv:1411.6724.

Scripts

Fig. 3 (b), derivatives of the convergence power spectrum with respect to various cosmological parameters.
cs_review_scripts.tgz.


Comments and suggestions are welcome! Please write to me at martin.kilbinger@cea.fr.

Last updated 22 July 2015.

A new model to predict weak-lensing peak counts I. Comparison with N-body Simulations

Authors: C.-A. Lin, M. Kilbinger.
Journal: A&A 576, A24
Year: 2015
Download: ADS | arXiv

 


Abstract

Weak-lensing peak counts has been shown to be a powerful tool for cosmology. It provides non-Gaussian information of large scale structures, complementary to second order statistics. We propose a new flexible method to predict weak lensing peak counts, which can be adapted to realistic scenarios, such as a real source distribution, intrinsic galaxy alignment, mask effects, photo-z errors from surveys, etc. The new model is also suitable for applying the tomography technique and non-linear filters. A probabilistic approach to model peak counts is presented. First, we sample halos from a mass function. Second, we assign them NFW profiles. Third, we place those halos randomly on the field of view. The creation of these "fast simulations" requires much less computing time compared to N-body runs. Then, we perform ray-tracing through these fast simulation boxes and select peaks from weak-lensing maps to predict peak number counts. The computation is achieved by our \textsc{Camelus} algorithm, which we make available at this http URL. We compare our results to N-body simulations to validate our model. We find that our approach is in good agreement with full N-body runs. We show that the lensing signal dominates shape noise and Poisson noise for peaks with SNR between 4 and 6. Also, counts from the same SNR range are sensitive to Ωm and σ8. We show how our model can discriminate between various combinations of those two parameters. In summary, we offer a powerful tool to study weak lensing peaks. The potential of our forward model is its high flexibility, making the use of peak counts under realistic survey conditions feasible.


Summary

A new, probabilistic model for weak-lensing peak counts is being proposed in this first paper of a series of three. The model is based on drawing halos from the mass function and, via ray-tracing, generating weak-lensing maps to count peaks. These simulated maps can directly be compared to observations, making this a forward-modelling approach of the cluster mass function, in contrast to many other traditional methods using cluster probes such as X-ray, optical richness, or SZ observations.

The model prediction is in very good agreement with N-body simulations.

It is very flexible, and can potentially include astrophysical and observational effects, such as intrinsic alignment, halo triaxiality, masking, photo-z errors, etc. Moreover, the pdf of the number of peaks can be output by the model, allowing for a very general likelihood calculation, without e.g. assuming a Gaussian distribution of the observables.

 

Review: Cosmology from cosmic shear observations

Mean and 68% error bars for the parameter  $\sigma_8 (\Omega_{\rm m}/0.3)^\alpha$, for various cosmic shear observations, plotted as function of their publication date (first arXiv submission). Data points are second-order statistics (circles), third-order (diamonds), 3D lensing (pentagons), galaxy-galaxy lensing (+ galaxy clustering; triangle), and CMB (squares).
Mean and 68% error bars for the parameter \sigma_8 (\Omega_{\rm m}/0.3)^\alpha, for various cosmic shear observations, plotted as function of their publication date (first arXiv submission). Data points are second-order statistics (circles), third-order (diamonds), 3D lensing (pentagons), galaxy-galaxy lensing (+ galaxy clustering; triangle), and CMB (squares).

A review on cosmology from cosmic shear observations has been submitted to ROPP, and has the arXiv reference arXiv:1411.0115. Comments are very welcome! Check also the accompanying web page for more information, updates, and errata.