peipei

Linear and non-linear Modified Gravity forecasts with future surveys

A new paper has been put on the arXiv by new CosmoStat member Valeria Pettorino, her PhD student Santiago Casas, in collaboration with Martin Kunz (Geneva) and Matteo Martinelli (Leiden).
The authors discuss forecasts in Modified Gravity cosmologies, described by two generic functions of time and space [Planck Dark Energy and Modified Gravity 2015Asaba et al 2013,Bull 2015Alonso et al 2016]. Their amplitude is constrained in different redshift bins. The authors elaborate on the impact of non-linear scales, showing that their inclusion (via a non-linear semi-analytical prescription applied to Modified Gravity) enables to highly reduce correlation among different redshift bins, even before any decorrelation procedure is applied. This is visually seen in the figure below (Fig.4 of arXiv), for the case of Galaxy Clustering: the correlation Matrix of the cosmological parameters (including the amplitudes of the Modified Gravity functions, binned in redshift)  is much more diagonal in the non-linear case (right panel) than in the linear one (left panel).

fig4_casasetal2017

A decorrelation procedure (Zero-phase Component Analysis, ZCA) is anyway used to extract those combinations which are best constrained by future surveys such as Euclid. With respect to Principal Component Analysis, ZCA allows to find a new vector of uncorrelated variables that is as similar as possible to the original vector of variables.

The authors further consider two smooth time functions whose main allowed to depart from General Relativity only at late times (late-time parameterization) or able to detach also at early times (early-time parameterization). The Fisher Matrix forecasts for standard and Modified gravity parameters, for different surveys (Euclid, SKA1, SKA2) is shown in the plot below (extracted from Fig.15 of arXiv), in which Galaxy Clustering and Weak Lensing probes are combined. Left panel refers to linear analysis, right panel includes a non-linear treatment.

fig15x4_casasetal2017fig15x6_casasetal2017 

 

K17_Fig1b

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.

Lieu-MT

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).
Sigma_tab_0715

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 06/16
Fig. 7 of the review article: The quantity \Sigma = \sigma_8 \left( \Omega_{\rm m}/0.3 \right)^\alpha as function of publication year.
Get the data in table format as pdf.
 
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.
 
 
 
 
 

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 & 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.

Fig4

New model on peak counts: paper published

 

Fig 1 from Lin & Kilbinger (2015)
Fig 1 from Lin & Kilbinger (2015)

A new, probabilistic model for weak-lensing peak counts has recently been proposed by CosmoStat group members Lin and Kilbinger (arXiv:1410.6955). It 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.

 

 

 

 

Fig 4 from Lin & Kilbinger (2015)
Fig 4 from Lin & Kilbinger (2015)

 

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.

 

The paper has been accepted for publication in A&A (20/01/2015). Reference: A&A, 576, A24.

The code corresponding to the model is available for download here.

peipei

Daniel Machado's PhD defense at CEA Saclay (2 pm, Galilée room)

Title: "Improving automated redshift detection in the low signal-to-noise regime for Large Sky Surveys"

Abstract: "Large redshift surveys of galaxies are key to pinning down cosmological models. We present the Darth Fader algorithm which is dedicated to tackling redshift estimation in the low signal to noise regime, & can blindly differentiate spectra into separate categories as to whether they are likely to yield accurate redshift results, or not. We additionally present a new method for continuum subtraction that does not rely on modelling.

Results are shown for simulated data derived from the COSMOS Mock Catalogue. Further results are shown for a test of the algorithm on a subset of the WiggleZ catalogue, where redshifts have previously been determined by visual inspection."

 

review1

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.

3482_1 (1)

Are the CMB anomalies real ?

Map of the CosmoStat secondary contributions to the diffuse background
Map of the CosmoStat secondary contributions to the diffuse background

A European team, involving researchers from the l'Ecole Polytechnique Fédérale de Lausanne (EPFL) and the Astrophysical Department Sap-AIM of CEA-Irfu, has found that some of the defects in the Cosmic Microwave Background of the universe present in the images obtained by the WMAP and Planck satellites may only be due to poor image reconstruction and incomplete subtraction of the contributions of our own galaxy. These results are published in the Journal of Cosmology and Astroparticle Physics August 2014.

GMCA_WPR1

Release of Planck + WMAP CMB map using sparsity.

Joint reconstruction from WMAP9 and Planck PR1 data with LGMCA
Joint reconstruction from WMAP9 and Planck PR1 data with LGMCA

The LGMCA method has been used to reconstruct the Cosmic Microwave Background (CMB) image from WMAP 9 year and Planck-PR1 data. Based on the sparse modeling of signals - a framework recently developed in applied mathematics - the proposed component separation method is well-suited for the extraction of foreground emissions.

A joint WMAP9 year and Planck PR1 CMB has been reconstructed for the first time and produce a very high quality CMB map, especially on the galactic center where it is the most difficult due to the strong foreground emissions of our Galaxy. This webpage provides some comparisons between the PR1 and WPR1 maps and codes to recompute the map in the spirit of reproducible research.

reduced_F3c

Reduced-shear power spectrum

Fitting formulae of the reduced-shear power spectrum for weak lensing

Reference

Martin Kilbinger, 2010, arXiv:1004.3493

Description

We provide fitting formulae for the reduced-shear power-spectrum correction which is third-order in the lensing potential. This correction reaches up to 10% of the total lensing spectrum. Higher-order correction terms are one order of magnitude below the third-order term. The correction involves an integral over the matter bispectrum. We fit this integral with a combination of power-law functions and polynomials. We also fit the derivatives with respect to cosmological parameters. A Taylor-expansion around a fiducial (WMAP7) model provides accurate reduced-shear corrections within a region in parameter space containing the WMAP7 68% error elllipsoid.

Results

Our fits are accurate to 1% for l<104, and to 2% for l<2·105, which reduces the bias by a factor of four compared to the case of no correction. This matches the precision lensing power spectrum predictions of recent N-body simulations.

Ratio of power spectra uncorrected (lower lines) and corrected (upper lines) for reduced-shear.

 

Download, install, and run the code

Download an example code which includes the fitting matrices. Use 'make' to compile the code. To use the code, you have to fill in Fmn(a) (eq. 10 from the paper) which involves the lensing efficiency, comoving distances and the redshift distribution(s).

The reduced-shear corrections are also implemented in the cosmology and lensing package 'nicaea'. This code provides all necessary functions to produce lensing observables (shear power spectrum and real-space second-order functions). The cosmology and redshift distributions are set via parameter files.

Author

Martin Kilbinger (martin.kilbinger@cea.fr)