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Aims:Calibrating the point spread function (PSF) is a fundamental part of weak gravitational lensing analyses. Even with corrected galaxy images, imperfect calibrations can introduce biases. We propose an analytical framework for quantifying PSF-induced systematics as diagnostics for cross-correlation measurements of weak lensing with density tracers, e.g., galaxy-galaxy lensing. We show how those systematics propagate to physical parameters of the density tracers. Those diagnostics only require a shape catalogue of PSF stars and foreground galaxy positions. Methods:We consider the PSF-induced multiplicative bias, and introduce three second-order statistics as additive biases. We compute both biases for the weak-lensing derived halo mass of spectroscopic foreground galaxy samples, in particular, their effect on the tangential shear and fitted halo mass as a function of stellar mass. In addition, we assess their impact on the recently published black-hole - halo-mass relation for type I Active Galactic Nuclei (AGNs). Results:Using weak-lensing catalogues from the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) and Dark Energy Survey (DES), we find the multiplicative biases in the tangential shear to be less than $0.5\%$. No correlations between additive bias and galaxy properties of the foreground sample are detected. The combined PSF systematics affect low-mass galaxies and small angular scales; halo mass estimates can be biased by up to 18$\%$ for a sample of central galaxies in the stellar mass range 9.0 $\leq$ log $M_*/\rm M_{\odot}$ < 9.5. Conclusions:The PSF-induced multiplicative bias is a subdominant contribution to current studies of weak-lensing - density cross-correlations, but might become significant for upcoming Stage-VI surveys. For samples with a low tangential shear, additive PSF systematics can induce a significant bias on derived properties such as halo mass., Comment: 11 pages, 5 figures

This letter presents, for the first time, direct constraints on the black-hole-to-halo-mass relation using weak gravitational lensing measurements. We construct type I and type II Active Galactic Nuclei (AGNs) samples from the Sloan Digital Sky Survey (SDSS), with a mean redshift of 0.4 0.1 for type I (type II) AGNs. This sample is cross-correlated with weak lensing shear from the Ultraviolet Near Infrared Northern Survey (UNIONS). We compute the excess surface mass density of the halos associated with $36,181$ AGNs from $94,308,561$ lensed galaxies and fit the halo mass in bins of black-hole mass. We find that more massive AGNs reside in more massive halos. We see no evidence of dependence on AGN type or redshift in the black-hole-to-halo-mass relationship when systematic errors in the measured black-hole masses are included. Our results are consistent with previous measurements for non-AGN galaxies. At a fixed black-hole mass, our weak-lensing halo masses are consistent with galaxy rotation curves, but significantly lower than galaxy clustering measurements. Finally, our results are broadly consistent with state-of-the-art hydro-dynamical cosmological simulations, providing a new constraint for black-hole masses in simulations., Comment: 14 pages, 5 figures. Submitted to ApJL

The accurate modelling of the Point Spread Function (PSF) is of paramount importance in astronomical observations, as it allows for the correction of distortions and blurring caused by the telescope and atmosphere. PSF modelling is crucial for accurately measuring celestial objects' properties. The last decades brought us a steady increase in the power and complexity of astronomical telescopes and instruments. Upcoming galaxy surveys like Euclid and LSST will observe an unprecedented amount and quality of data. Modelling the PSF for these new facilities and surveys requires novel modelling techniques that can cope with the ever-tightening error requirements. The purpose of this review is three-fold. First, we introduce the optical background required for a more physically-motivated PSF modelling and propose an observational model that can be reused for future developments. Second, we provide an overview of the different physical contributors of the PSF, including the optic- and detector-level contributors and the atmosphere. We expect that the overview will help better understand the modelled effects. Third, we discuss the different methods for PSF modelling from the parametric and non-parametric families for ground- and space-based telescopes, with their advantages and limitations. Validation methods for PSF models are then addressed, with several metrics related to weak lensing studies discussed in detail. Finally, we explore current challenges and future directions in PSF modelling for astronomical telescopes., Comment: 64 pages, 14 figures. Accepted to Frontiers in Astronomy and Space Sciences

We consider coupled dark energy (CDE) cosmologies, where dark matter particles feel a force stronger than gravity, due to the fifth force mediated by a scalar field which plays the role of dark energy. We perform for the first time a tomographic analysis of coupled dark energy, where the coupling strength is parametrized and constrained in different redshift bins. This allows us to verify which data can better constrain the strength of the coupling and how large the coupling can be at different epochs. First, we employ cosmic microwave background data from Planck, the Atacama Cosmology Telescope (ACT) and South Pole Telescope (SPT), showing the impact of different choices that can be done in combining these datasets. Then, we use a range of low redshift probes to test CDE cosmologies, both for a constant and for a tomographic coupling. In particular, we use for the first time data from weak lensing (the KiDS-1000 survey), galaxy clustering (BOSS survey), and their combination, including 3x2pt galaxy-galaxy lensing cross-correlation data. We do not find evidence for nonzero coupling, either for a constant or tomographic case. A nonzero coupling is however still in agreement with current data. For CMB and background datasets, a tomographic coupling allows for $\beta$ values up to one order of magnitude larger than in previous works, in particular at $z<1$. The use of 3x2pt analysis then becomes important to constrain $\beta$ at low redshifts, even when coupling is allowed to vary: for 3x2pt we find, at $0.5 < z < 1$, $\beta=0.0180_{-0.011}^{+0.007}$, comparable to what CMB and background datasets would give for a constant coupling. This makes upcoming galaxy surveys potentially powerful probes to test CDE models at low redshifts. (abridged), Comment: 25 pages, 17 figures. Accepted for publication in Physical Review D

Cold dark matter haloes are expected to be triaxial, and so appear elliptical in projection. We use weak gravitational lensing from the Canada-France Imaging Survey (CFIS) component of the Ultraviolet-Near Infrared Optical Northern Survey (UNIONS) to measure the ellipticity of the dark matter haloes around Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Data Release 7 (DR7) and from the CMASS and LOWZ samples of the Baryon Oscillation Spectroscopic Survey (BOSS), assuming their major axes are aligned with the stellar light. We find that DR7 LRGs with masses $M \sim 2.7\times10^{13} \mathrm{M}_{\odot}/h$ have halo ellipticities $e=0.46\pm0.10$. Expressed as a fraction of the galaxy ellipticity, we find $f_h = 2.2\pm0.6$. For BOSS LRGs, the detection is of marginal significance: $e = 0.20\pm0.10$ and $f_h=0.7\pm0.7$. These results are in agreement with other measurements of halo ellipticity from weak lensing and, taken together with previous results, suggest an increase of halo ellipticity of $0.10\pm0.06$ per decade in halo mass. This trend agrees with the predictions from hydrodynamical simulations, which find that at higher halo masses, not only do dark matter haloes become more elliptical, but that the misalignment between major axis of the stellar light in the central galaxy and that of the dark matter decreases., Comment: MNRAS, accepted

UNIONS is an ongoing deep photometric multi-band survey of the Northern sky. As part of UNIONS, CFIS provides r-band data which we use to study weak-lensing peak counts for cosmological inference. We assess systematic effects for weak-lensing peak counts and their impact on cosmological parameters for the UNIONS survey. In particular, we present results on local calibration, metacalibration shear bias, baryonic feedback, the source galaxy redshift estimate, intrinsic alignment, and the cluster member dilution. For each uncertainty and systematic effect, we describe our mitigation scheme and the impact on cosmological parameter constraints. We obtain constraints on cosmological parameters from MCMC using CFIS data and MassiveNuS N-body simulations as a model for peak counts statistics. Depending on the calibration (local versus global, and the inclusion of the residual multiplicative shear bias), the mean matter density parameter $\Omega_m$ can shift up to $-0.024$ ($-0.5\sigma$). We also see that including baryonic corrections can shift $\Omega_m$ by $+0.027$ ($+0.5 \sigma$) with respect to the DM-only simulations. Reducing the impact of the intrinsic alignment and cluster member dilution through signal-to-noise cuts can lead to a shift in $\Omega_m$ of $+0.027$ ($+0.5 \sigma$). Finally, with a mean redshift uncertainty of $\Delta \bar{z} = 0.03$, we see that the shift of $\Omega_m$ ($+0.001$ which corresponds to $+0.02 \sigma$) is not significant. This paper investigates for the first time with UNIONS weak-lensing data and peak counts the impact of systematic effects. The value of $\Omega_m$ is the most impacted and can shift up to $\sim 0.03$ which corresponds to $0.5\sigma$ depending on the choices for each systematics. We expect constraints to become more reliable with future (larger) data catalogues, for which the current pipeline will provide a starting point., Comment: 19 pages, 19 figures

UNIONS is an ongoing collaboration that will provide the largest deep photometric survey of the Northern sky in four optical bands to date. As part of this collaboration, CFIS is taking $r$-band data with an average seeing of 0.65 arcsec, which is complete to magnitude 24.5 and thus ideal for weak-lensing studies. We perform the first weak-lensing analysis of CFIS $r$-band data over an area spanning 1700 deg$^2$ of the sky. We create a catalogue with measured shapes for 40 million galaxies, corresponding to an effective density of 6.8 galaxies per square arcminute, and demonstrate a low level of systematic biases. This work serves as the basis for further cosmological studies using the full UNIONS survey of 4800 deg$^2$ when completed. Here we present ShapePipe, a newly developed weak-lensing pipeline. This pipeline makes use of state-of-the-art methods such as Ngmix for accurate galaxy shape measurement. Shear calibration is performed with metacalibration. We carry out extensive validation tests on the Point Spread Function (PSF), and on the galaxy shapes. In addition, we create realistic image simulations to validate the estimated shear. We quantify the PSF model accuracy and show that the level of systematics is low as measured by the PSF residuals. Their effect on the shear two-point correlation function is sub-dominant compared to the cosmological contribution on angular scales <100 arcmin. The additive shear bias is below 5x$10^{-4}$, and the residual multiplicative shear bias is at most $10^{-3}$ as measured on image simulations. Using COSEBIs we show that there are no significant B-modes present in second-order shear statistics. We present convergence maps and see clear correlations of the E-mode with known cluster positions. We measure the stacked tangential shear profile around Planck clusters at a significance higher than $4\sigma$.

In astronomy, upcoming space telescopes with wide-field optical instruments have a spatially varying point spread function (PSF). Specific scientific goals require a high-fidelity estimation of the PSF at target positions where no direct measurement of the PSF is provided. Even though observations of the PSF are available at some positions of the field of view (FOV), they are undersampled, noisy, and integrated into wavelength in the instrument's passband. PSF modeling represents a challenging ill-posed problem, as it requires building a model from degraded observations that can infer a super-resolved PSF at any wavelength and position in the FOV. Our model, coined WaveDiff, proposes a paradigm shift in the data-driven modeling of the point spread function field of telescopes. We change the data-driven modeling space from the pixels to the wavefront by adding a differentiable optical forward model into the modeling framework. This change allows the transfer of complexity from the instrumental response into the forward model. The proposed model relies on stochastic gradient descent to estimate its parameters. Our framework paves the way to building powerful, physically motivated models that do not require special calibration data. This paper demonstrates the WaveDiff model in a simplified setting of a space telescope. The proposed framework represents a performance breakthrough with respect to the existing state-of-the-art data-driven approach. The pixel reconstruction errors decrease 6-fold at observation resolution and 44-fold for a 3x super-resolution. The ellipticity errors are reduced at least 20 times, and the size error is reduced more than 250 times. By only using noisy broad-band in-focus observations, we successfully capture the PSF chromatic variations due to diffraction. Code available at https://github.com/tobias-liaudat/wf-psf., Comment: Submitted. Without appendix: 42 pages, 10 figures, 4 tables

Weak gravitational lensing is one of the few direct methods to map the dark-matter distribution on large scales in the Universe, and to estimate cosmological parameters. We study a Bayesian inference problem where the data covariance $\mathbf{C}$, estimated from a number $n_{\textrm{s}}$ of numerical simulations, is singular. In a cosmological context of large-scale structure observations, the creation of a large number of such $N$-body simulations is often prohibitively expensive. Inference based on a likelihood function often includes a precision matrix, $\Psi = \mathbf{C}^{-1}$. The covariance matrix corresponding to a $p$-dimensional data vector is singular for $p \ge n_{\textrm{s}}$, in which case the precision matrix is unavailable. We propose the likelihood-free inference method Approximate Bayesian Computation (ABC) as a solution that circumvents the inversion of the singular covariance matrix. We present examples of increasing degree of complexity, culminating in a realistic cosmological scenario of the determination of the weak-gravitational lensing power spectrum for the upcoming European Space Agency satellite Euclid. While we found the ABC parameter estimate variances to be mildly larger compared to likelihood-based approaches, which are restricted to settings with $p < n_{\textrm{s}}$, we obtain unbiased parameter estimates with ABC even in extreme cases where $p / n_{\textrm{s}} \gg 1$. The code has been made publicly available to ensure the reproducibility of the results., Comment: 29 pages, 8 figures, 3 tables. Accepted by Astronomy and Computing. Code publicly available at https://github.com/emilleishida/CorrMatrix_ABC

We propose a paradigm shift in the data-driven modeling of the instrumental response field of telescopes. By adding a differentiable optical forward model into the modeling framework, we change the data-driven modeling space from the pixels to the wavefront. This allows to transfer a great deal of complexity from the instrumental response into the forward model while being able to adapt to the observations, remaining data-driven. Our framework allows a way forward to building powerful models that are physically motivated, interpretable, and that do not require special calibration data. We show that for a simplified setting of a space telescope, this framework represents a real performance breakthrough compared to existing data-driven approaches with reconstruction errors decreasing 5 fold at observation resolution and more than 10 fold for a 3x super-resolution. We successfully model chromatic variations of the instrument's response only using noisy broad-band in-focus observations., Comment: 10 pages. Accepted for the Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021)

We present a search for disturbed, candidate ram pressure stripping galaxies across more than 50 spectroscopically selected SDSS groups and clusters. Forty-eight ram pressure candidates are visually identified in these systems using high quality UNIONS imaging from the Canada-France Hawaii Telescope, covering ~6200 and ~2800 square degrees in the u- and r-bands respectively. Ram pressure candidates are found in groups and clusters spanning a wide range in halo mass and include ~30 ram pressure candidates in the group regime ($M_h < 10^{14}$). The observed frequency of ram pressure candidates shows substantial scatter with group/cluster mass, but on average is larger in clusters ($M_h > 10^{14}\,M_\odot$) than groups ($M_h < 10^{14}\,M_\odot$) by a factor of ~2. We find that ram pressure candidates are most commonly low-mass galaxies and have enhanced star formation rates relative to star-forming field galaxies. The enhancement in star formation is largely independent of galaxy mass and strongest for galaxies in clusters. As a result of the large survey footprint and excellent image quality from UNIONS, we are able to identify disturbed galaxies, potentially affected by ram pressure stripping, across a wide range of host environment., Comment: 12 pages, 9 figures, 1 appendix, accepted for publication in MNRAS

We present a new shear calibration method based on machine learning. The method estimates the individual shear responses of the objects from the combination of several measured properties on the images using supervised learning. The supervised learning uses the true individual shear responses obtained from copies of the image simulations with different shear values. On simulated GREAT3data, we obtain a residual bias after the calibration compatible with 0 and beyond Euclid requirements for a signal-to-noise ratio > 20 within ~15 CPU hours of training using only ~10^5 objects. This efficient machine-learning approach can use a smaller data set because the method avoids the contribution from shape noise. The low dimensionality of the input data also leads to simple neural network architectures. We compare it to the recently described method Metacalibration, which shows similar performances. The different methods and systematics suggest that the two methods are very good complementary methods. Our method can therefore be applied without much effort to any survey such as Euclid or the Vera C. Rubin Observatory, with fewer than a million images to simulate to learn the calibration function., Comment: 16 pages, 1 table, 13 figures

We present a weak-lensing analysis of X-ray galaxy groups and clusters selected from the XMM-XXL survey using the first-year data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program. Our joint weak-lensing and X-ray analysis focuses on 136 spectroscopically confirmed X-ray-selected systems at 0.031 < z < 1.033 detected in the 25sqdeg XXL-N region. We characterize the mass distributions of individual clusters and establish the concentration-mass (c-M) relation for the XXL sample, by accounting for selection bias and statistical effects, and marginalizing over the remaining mass calibration uncertainty. We find the mass-trend parameter of the c-M relation to be \beta = -0.07 \pm 0.28 and the normalization to be c200 = 4.8 \pm 1.0 (stat) \pm 0.8 (syst) at M200=10^{14}Msun/h and z = 0.3. We find no statistical evidence for redshift evolution. Our weak-lensing results are in excellent agreement with dark-matter-only c-M relations calibrated for recent LCDM cosmologies. The level of intrinsic scatter in c200 is constrained as \sigma(\ln[c200]) < 24% (99.7% CL), which is smaller than predicted for the full population of LCDM halos. This is likely caused in part by the X-ray selection bias in terms of the relaxation state. We determine the temperature-mass (Tx-M500) relation for a subset of 105 XXL clusters that have both measured HSC lensing masses and X-ray temperatures. The resulting Tx-M500 relation is consistent with the self-similar prediction. Our Tx-M500 relation agrees with the XXL DR1 results at group scales, but has a slightly steeper mass trend, implying a smaller mass scale in the cluster regime. The overall offset in the Tx-M500 relation is at the $1.5\sigma$ level, corresponding to a mean mass offset of (34\pm 20)%. We also provide bias-corrected, weak-lensing-calibrated M200 and M500 mass estimates of individual XXL clusters based on their measured X-ray temperatures., Comment: Version matching the one published in ApJ. We recommend to use statistically corrected mass estimates (M200MT, M500MT) of Table 2 for a given individual cluster. One of two companion papers presenting initial HSC-XXL results (Mauro Sereno et al., arXiv:1912.02827)

In this manuscript of the habilitation \`a diriger des recherches (HDR), the author presents some of his work over the last ten years. The main topic of this thesis is cosmic shear, the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure. I review the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then I give an overview of weak-lensing measurements, and present observational results from the Canada-France Hawai'i Lensing Survey (CFHTLenS), as well as the implications for cosmology. I conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations., Comment: Manuscript of the habilitation \`a diriger des recherches, required for supervising students in the French university system. 61 pages, text in English. Substantial overlap with arXiv:1411.0115

We present a new method to estimate shear measurement bias in image simulations that significantly improves the precision with respect to current techniques. Our method is based on measuring the shear response for individual images. We generated sheared versions of the same image to measure how the galaxy shape changes with the small applied shear. This shear response is the multiplicative shear bias for each image. In addition, we also measured the individual additive bias. Using the same noise realizations for each sheared version allows us to compute the shear response at very high precision. The estimated shear bias of a sample of galaxies is then the average of the individual measurements. The precision of this method leads to an improvement with respect to previous methods concerned with the precision of estimates of multiplicative bias since our method is not affected by noise from shape measurements, which until now has been the dominant uncertainty. As a consequence, the method does not require shape-noise suppression for a precise estimation of shear multiplicative bias. Our method can be readily used for numerous 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., Comment: 14 pages, 10 figures

We present a study of the dependencies of shear bias on simulation (input) and measured (output) parameters, noise, point-spread function anisotropy, pixel size, and the model bias coming from two different and independent galaxy shape estimators. We used simulated images from Galsim based on the GREAT3 control-space-constant branch, and we measured shear bias from a model-fitting method (gFIT) and a moment-based method (Kaiser-Squires-Broadhurst). We show the bias dependencies found on input and output parameters for both methods, and we identify the main dependencies and causes. Most of the results are consistent between the two estimators, an interesting result given the differences of the methods. We also find important dependences on orientation and morphology properties such as flux, size, and ellipticity. We show that noise and pixelization play an important role in the bias dependencies on the output properties and galaxy orientation. We show some examples of model bias that produce a bias dependence on the Sersic index n as well as a different shear bias between galaxies consisting of a single Sersic profile and galaxies with a disc and a bulge. We also see an important coupling between several properties on the bias dependences. Because of this, we need to study several measured properties simultaneously in order to properly understand the nature of shear bias. This paper serves as a first step towards a companion paper that describes a machine learning approach to modelling shear bias as a complex function of many observed properties., Comment: 13 pages, 7 figures

Weak-lensing peak counts provide a straightforward way to constrain cosmology by linking local maxima of the lensing signal to the mass function. Recent applications to data have already been numerous and fruitful. However, the importance of understanding and dealing with systematics increases as data quality reaches an unprecedented level. One of the sources of systematics is the convergence-shear inversion. This effect, inevitable when carrying out a convergence field from observations, is usually neglected by theoretical peak models. Thus, it could have an impact on cosmological results. In this paper, we study the bias from neglecting (mis-modeling) the inversion. Our tests show a small but non-negligible bias. The cosmological dependence of this bias seems to be related to the parameter Sigma_8. When this bias propagates to the parameter estimation, we discovered that constraint contours involving the dark energy equation of state can differ by 2-sigma. Such an effect can be even larger for future high-precision surveys and we argue that the inversion should be properly modeled for theoretical peak models., Comment: 6 pages, 4 figures. Conformed to the published version

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 is negligible when constraining cosmological parameters from current weak lensing surveys. This is demonstrated using data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We find that the reported tension with Planck Cosmic Microwave Background (CMB) temperature anisotropy results cannot be alleviated. 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., Comment: 17 pages, 5 figures, 2 tables. Matches published version (MNRAS, 2017, 472, 2126)

Peak statistics in weak lensing maps access the non-Gaussian information contained in the large-scale distribution of matter in the Universe. They are therefore a promising complement to two-point and higher-order statistics to constrain our cosmological models. To prepare for the high-precision data of next-generation surveys, we assess the constraining power of peak counts in a simulated Euclid-like survey on the cosmological parameters $\Omega_\mathrm{m}$, $\sigma_8$, and $w_0^\mathrm{de}$. In particular, we study how the Camelus model--a fast stochastic algorithm for predicting peaks--can be applied to such large surveys. We measure the peak count abundance in a mock shear catalogue of ~5,000 sq. deg. using a multiscale mass map filtering technique. We then constrain the parameters of the mock survey using Camelus combined with approximate Bayesian computation (ABC). We find that peak statistics yield a tight but significantly biased constraint in the $\sigma_8$-$\Omega_\mathrm{m}$ plane, indicating the need to better understand and control the model's systematics. We calibrate the model to remove the bias and compare results to those from the two-point correlation functions (2PCF) measured on the same field. In this case, we find the derived parameter $\Sigma_8=\sigma_8(\Omega_\mathrm{m}/0.27)^\alpha=0.76_{-0.03}^{+0.02}$ with $\alpha=0.65$ for peaks, while for 2PCF the value is $\Sigma_8=0.76_{-0.01}^{+0.02}$ with $\alpha=0.70$. We therefore see comparable constraining power between the two probes, and the offset of their $\sigma_8$-$\Omega_\mathrm{m}$ degeneracy directions suggests that a combined analysis would yield tighter constraints than either measure alone. As expected, $w_0^\mathrm{de}$ cannot be well constrained without a tomographic analysis, but its degeneracy directions with the other two varied parameters are still clear for both peaks and 2PCF. (abridged), Comment: 12 pages, 10 figures, submitted to A&A

DESI (Dark Energy Spectroscopic Instrument) is a Stage IV ground-based dark energy experiment that will study baryon acoustic oscillations (BAO) and the growth of structure through redshift-space distortions with a wide-area galaxy and quasar redshift survey. To trace the underlying dark matter distribution, spectroscopic targets will be selected in four classes from imaging data. We will measure luminous red galaxies up to $z=1.0$. To probe the Universe out to even higher redshift, DESI will target bright [O II] emission line galaxies up to $z=1.7$. Quasars will be targeted both as direct tracers of the underlying dark matter distribution and, at higher redshifts ($ 2.1 < z < 3.5$), for the Ly-$\alpha$ forest absorption features in their spectra, which will be used to trace the distribution of neutral hydrogen. When moonlight prevents efficient observations of the faint targets of the baseline survey, DESI will conduct a magnitude-limited Bright Galaxy Survey comprising approximately 10 million galaxies with a median $z\approx 0.2$. In total, more than 30 million galaxy and quasar redshifts will be obtained to measure the BAO feature and determine the matter power spectrum, including redshift space distortions.

DESI (Dark Energy Spectropic Instrument) is a Stage IV ground-based dark energy experiment that will study baryon acoustic oscillations and the growth of structure through redshift-space distortions with a wide-area galaxy and quasar redshift survey. The DESI instrument is a robotically-actuated, fiber-fed spectrograph capable of taking up to 5,000 simultaneous spectra over a wavelength range from 360 nm to 980 nm. The fibers feed ten three-arm spectrographs with resolution $R= \lambda/\Delta\lambda$ between 2000 and 5500, depending on wavelength. The DESI instrument will be used to conduct a five-year survey designed to cover 14,000 deg$^2$. This powerful instrument will be installed at prime focus on the 4-m Mayall telescope in Kitt Peak, Arizona, along with a new optical corrector, which will provide a three-degree diameter field of view. The DESI collaboration will also deliver a spectroscopic pipeline and data management system to reduce and archive all data for eventual public use.

This is the third in a series of papers that develop a new and flexible model to predict weak-lensing (WL) peak counts, which have been shown to be a very valuable non-Gaussian probe of cosmology. In this paper, we compare the cosmological information extracted from WL peak counts using different filtering techniques of the galaxy shear data, including linear filtering with a Gaussian and two compensated filters (the starlet wavelet and the aperture mass), and the nonlinear filtering method MRLens. We present improvements to our model that account for realistic survey conditions, which are masks, shear-to-convergence transformations, and non-constant noise. We create simulated peak counts from our stochastic model, from which we obtain constraints on the matter density $\Omega_\mathrm{m}$, the power spectrum normalisation $\sigma_8$, and the dark-energy parameter $w_0$. We use two methods for parameter inference, a copula likelihood, and approximate Bayesian computation (ABC). We measure the contour width in the $\Omega_\mathrm{m}$-$\sigma_8$ degeneracy direction and the figure of merit to compare parameter constraints from different filtering techniques. We find that starlet filtering outperforms the Gaussian kernel, and that including peak counts from different smoothing scales helps to lift parameter degeneracies. Peak counts from different smoothing scales with a compensated filter show very little cross-correlation, and adding information from different scales can therefore strongly enhance the available information. Measuring peak counts separately from different scales yields tighter constraints than using a combined peak histogram from a single map that includes multiscale information. Our results suggest that a compensated filter function with counts included separately from different smoothing scales yields the tightest constraints on cosmological parameters from WL peaks., Comment: 14 pages, 12 figures, published version

The XXL survey is the largest survey carried out by XMM-Newton. Covering an area of 50deg$^2$, the survey contains $\sim450$ galaxy clusters out to a redshift $\sim$2 and to an X-ray flux limit of $\sim5\times10^{-15}erg\,s^{-1}cm^{-2}$. This paper is part of the first release of XXL results focussed on the bright cluster sample. We investigate the scaling relation between weak-lensing mass and X-ray temperature for the brightest clusters in XXL. The scaling relation is used to estimate the mass of all 100 clusters in XXL-100-GC. Based on a subsample of 38 objects that lie within the intersection of the northern XXL field and the publicly available CFHTLenS catalog, we derive the $M_{WL}$ of each system with careful considerations of the systematics. The clusters lie at $0.1

We present weak lensing constraints on the ellipticity of galaxy-scale matter haloes and the galaxy-halo misalignment. Using data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), we measure the weighted-average ratio of the aligned projected ellipticity components of galaxy matter haloes and their embedded galaxies, $f_\mathrm{h}$, split by galaxy type. We then compare our observations to measurements taken from the Millennium Simulation, assuming different models of galaxy-halo misalignment. Using the Millennium Simulation we verify that the statistical estimator used removes contamination from cosmic shear. We also detect an additional signal in the simulation, which we interpret as the impact of intrinsic shape-shear alignments between the lenses and their large-scale structure environment. These alignments are likely to have caused some of the previous observational constraints on $f_\mathrm{h}$ to be biased high. From CFHTLenS we find $f_\mathrm{h}=-0.04 \pm 0.25$ for early-type galaxies, which is consistent with current models for the galaxy-halo misalignment predicting $f_\mathrm{h}\simeq 0.20$. For late-type galaxies we measure $f_\mathrm{h}=0.69_{-0.36}^{+0.37}$ from CFHTLenS. This can be compared to the simulated results which yield $f_\mathrm{h}\simeq 0.02$ for misaligned late-type models., Comment: 21 pages, 3 tables, 9 figures. This replacement matches the version accepted for publication in MNRAS

Peak counts have been shown to be an excellent tool to extract the non-Gaussian part of the weak lensing signal. Recently, we developped a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analyses. In this work, we explore and compare various strategies for constraining parameter using our model, focusing on the matter density $\Omega_\mathrm{m}$ and the density fluctuation amplitude $\sigma_8$. First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analysis with the copula likelihood, a technique which makes a weaker assumption compared to the Gaussian likelihood. Third, direct, non-analytic parameter estimations are applied using the full information of the distribution. Fourth, we obtain constraints with approximate Bayesian computation (ABC), an efficient, robust, and likelihood-free algorithm based on accept-reject sampling. We find that neglecting the CDC effect enlarges parameter contours by 22%, and that the covariance-varying copula likelihood is a very good approximation to the true likelihood. The direct techniques work well in spite of noisier contours. Concerning ABC, the iterative process converges quickly to a posterior distribution that is in an excellent agreement with results from our other analyses. The time cost for ABC is reduced by two orders of magnitude. The stochastic nature of our weak-lensing peak count model allows us to use various techniques that approach the true underlying probability distribution of observables, without making simplifying assumptions. Our work can be generalized to other observables where forward simulations provide samples of the underlying distribution., Comment: 15 pages, 11 figures. Accepted version

We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically-varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially-varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by $\sim 1$ per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the S\'{e}rsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity., Comment: 32 pages + 15 pages of technical appendices; 28 figures; published in MNRAS; all data and other information may be found at https://github.com/barnabytprowe/great3-public as the GREAT3 website and leaderboard are no longer live. v3 has updates to this comment only

Cosmic shear is the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Such images are coherently deformed by the tidal field of matter inhomogeneities along the line of sight. By measuring galaxy shape correlations, we can study the properties and evolution of structure on large scales as well as the geometry of the Universe. Thus, cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure. We review here the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then we give an overview of weak-lensing measurements, and present the main observational cosmic-shear results since it was discovered 15 years ago, as well as the implications for cosmology. We then conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations., Comment: 65 pages (single column format), 12 figures, 1 table. Corresponds to published version by RoPP (in double column format; 39 pages). For a video abstract see https://www.youtube.com/watch?v=R-ECFixOca0

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 http://www.cosmostat.org/software/camelus/ . 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 $\Omega_\mathrm{m}$ and $\sigma_8$. 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., Comment: 10 pages, 7 figures. Our code is available at http://www.cosmostat.org/software/camelus/ . Published version

Using a sample of 25683 star-forming and 2821 passive galaxies at $z\sim2$, selected in the COSMOS field following the BzK color criterion, we study the hosting halo mass and environment of galaxies as a function of their physical properties. Spitzer and Herschel provide accurate SFR estimates for starburst galaxies. We measure the auto- and cross-correlation functions of various galaxy sub-samples and infer the properties of their hosting halos using both an HOD model and the linear bias at large scale. We find that passive and star-forming galaxies obey a similarly rising relation between the halo and stellar mass. The mean host halo mass of star forming galaxies increases with the star formation rate between 30 and 200 M$_\odot$.yr$^{-1}$, but flattens for higher values, except if we select only main-sequence galaxies. This reflects the expected transition from a regime of secular co-evolution of the halos and the galaxies to a regime of episodic starburst. We find similar large scale biases for main-sequence, passive, and starburst galaxies at equal stellar mass, suggesting that these populations live in halos of the same mass. We detect an excess of clustering on small scales for passive galaxies and showed, by measuring the large-scale bias of close pairs, that this excess is caused by a small fraction ($\sim16%$) of passive galaxies being hosted by massive halos ($\sim 3 \times 10^{13}$ M$_\odot$) as satellites. Finally, extrapolating the growth of halos hosting the z$\sim$2 population, we show that M$_\star \sim 10^{10}$ M$_\odot$ galaxies at z$\sim$2 will evolve, on average, into massive (M$_\star \sim 10^{11}$ M$_\odot$), field galaxies in the local Universe and M$_\star \sim 10^{11}$ M$_\odot$ galaxies at z=2 into local, massive, group galaxies. The most massive main-sequence galaxies and close pairs of massive, passive galaxies end up in today's clusters., Comment: 18 pages, 16 figures, Accepted by A&A

Higher-order, non-Gaussian aspects of the large-scale structure carry valuable information on structure formation and cosmology, which is complementary to second-order statistics. In this work we measure second- and third-order weak-lensing aperture-mass moments from CFHTLenS and combine those with CMB anisotropy probes. The third moment is measured with a significance of $2\sigma$. The combined constraint on $\Sigma_8 = \sigma_8 (\Omega_{\rm m}/0.27)^\alpha$ is improved by 10%, in comparison to the second-order only, and the allowed ranges for $\Omega_{\rm m}$ and $\sigma_8$ are substantially reduced. Including general triangles of the lensing bispectrum yields tighter constraints compared to probing mainly equilateral triangles. Second- and third-order CFHTLenS lensing measurements improve Planck CMB constraints on $\Omega_{\rm m}$ and $\sigma_8$ by 26% for flat $\Lambda$CDM. For a model with free curvature, the joint CFHTLenS-Planck result is $\Omega_{\rm m} = 0.28 \pm 0.02$ (68% confidence), which is an improvement of 43% compared to Planck alone. We test how our results are potentially subject to three astrophysical sources of contamination: source-lens clustering, the intrinsic alignment of galaxy shapes, and baryonic effects. We explore future limitations of the cosmological use of third-order weak lensing, such as the nonlinear model and the Gaussianity of the likelihood function., Comment: Accepted by MNRAS. 21 pages, 14 figues, 8 tables. The data is available at http://www.cfhtlens.org . The software used for the cosmological analysis can be downloaded from http://cosmopmc.info

We present the observational evidence of the 2-halo term in the stacked shear profile of a sample of about 1200 optically selected galaxy clusters based on imaging data and the public shear catalog from the CFHTLenS. We find that the halo bias, a measure of the correlated distribution of matter around galaxy clusters, has amplitude and correlation with galaxy cluster mass in very good agreement with the predictions based on the LCDM standard cosmological model. The mass-concentration relation is flat but higher than theoretical predictions. We also confirm the close scaling relation between the optical richness of galaxy clusters and their mass., Comment: 5 pages, 4 figures. In press on ApJ Letters

We present a finely-binned tomographic weak lensing analysis of the Canada-France-Hawaii Telescope Lensing Survey, CFHTLenS, mitigating contamination to the signal from the presence of intrinsic galaxy alignments via the simultaneous fit of a cosmological model and an intrinsic alignment model. CFHTLenS spans 154 square degrees in five optical bands, with accurate shear and photometric redshifts for a galaxy sample with a median redshift of zm =0.70. We estimate the 21 sets of cosmic shear correlation functions associated with six redshift bins, each spanning the angular range of 1.5

We present a quantitative analysis of the largest contiguous maps of projected mass density obtained from gravitational lensing shear. We use data from the 154 deg2 covered by the Canada-France-Hawaii Telescope Lensing Survey. Our study is the first attempt to quantitatively characterize the scientific value of lensing maps, which could serve in the future as a complementary approach to the study of the dark universe with gravitational lensing. We show that mass maps contain unique cosmological information beyond that of traditional two-points statistical analysis techniques. Using a series of numerical simulations, we first show how, reproducing the CFHTLenS observing conditions, gravitational lensing inversion provides a reliable estimate of the projected matter distribution of large scale structure. We validate our analysis by quantifying the robustness of the maps with various statistical estimators. We then apply the same process to the CFHTLenS data. We find that the 2-points correlation function of the projected mass is consistent with the cosmological analysis performed on the shear correlation function discussed in the CFHTLenS companion papers. The maps also lead to a significant measurement of the third order moment of the projected mass, which is in agreement with analytic predictions, and to a marginal detection of the fourth order moment. Tests for residual systematics are found to be consistent with zero for the statistical estimators we used. A new approach for the comparison of the reconstructed mass map to that predicted from the galaxy distribution reveals the existence of giant voids in the dark matter maps as large as 3 degrees on the sky. Our analysis shows that lensing mass maps can be used for new techniques such as peak statistics and the morphological analysis of the projected dark matter distribution., Comment: Version accepted by MNRAS

We present the strongest robust constraints on primordial non-Gaussianity (PNG) from currently available galaxy surveys, combining large-scale clustering measurements and their cross-correlations with the cosmic microwave background. We update the data sets used by Giannantonio et al. (2012), and broaden that analysis to include the full set of two-point correlation functions between all surveys. In order to obtain the most reliable constraints on PNG, we advocate the use of the cross-correlations between the catalogs as a robust estimator and we perform an extended analysis of the possible systematics to reduce their impact on the results. To minimize the impact of stellar contamination in our luminous red galaxy (LRG) sample, we use the recent Baryon Oscillations Spectroscopic Survey catalog of Ross et al. (2011). We also find evidence for a new systematic in the NVSS radio galaxy survey similar to, but smaller than, the known declination-dependent issue; this is difficult to remove without affecting the inferred PNG signal, and thus we do not include the NVSS auto-correlation function in our analyses. We find no evidence of primordial non-Gaussianity; for the local-type configuration we obtain for the skewness parameter $ -36 < f_{\mathrm{NL}} < 45 $ at 95 % c.l. ($5 \pm 21$ at $1\sigma$) when using the most conservative part of our data set, improving previous results; we also find no evidence for significant kurtosis, parameterized by $g_{\mathrm{NL}}$. In addition to PNG, we simultaneously constrain dark energy and find that it is required with a form consistent with a cosmological constant., Comment: 24 pages, 16 figures. More conservative treatment of the NVSS data, version accepted by Phys. Rev. D

The Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) comprises deep multi-colour (u*g'r'i'z') photometry spanning 154 square degrees, with accurate photometric redshifts and shape measurements. We demonstrate that the redshift probability distribution function summed over galaxies provides an accurate representation of the galaxy redshift distribution accounting for random and catastrophic errors for galaxies with best fitting photometric redshifts z_p < 1.3. We present cosmological constraints using tomographic weak gravitational lensing by large-scale structure. We use two broad redshift bins 0.5 < z_p <= 0.85 and 0.85 < z_p <= 1.3 free of intrinsic alignment contamination, and measure the shear correlation function on angular scales in the range ~1-40 arcmin. We show that the problematic redshift scaling of the shear signal, found in previous CFHTLS data analyses, does not afflict the CFHTLenS data. For a flat Lambda-CDM model and a fixed matter density Omega_m=0.27, we find the normalisation of the matter power spectrum sigma_8=0.771 \pm 0.041. When combined with cosmic microwave background data (WMAP7), baryon acoustic oscillation data (BOSS), and a prior on the Hubble constant from the HST distance ladder, we find that CFHTLenS improves the precision of the fully marginalised parameter estimates by an average factor of 1.5-2. Combining our results with the above cosmological probes, we find Omega_m=0.2762 \pm 0.0074 and sigma_8=0.802 \pm 0.013., Comment: 17 pages, 12 figures, submitted to MNRAS

Dark energy may be the first sign of new fundamental physics in the Universe, taking either a physical form or revealing a correction to Einsteinian gravity. Weak gravitational lensing and galaxy peculiar velocities provide complementary probes of General Relativity, and in combination allow us to test modified theories of gravity in a unique way. We perform such an analysis by combining measurements of cosmic shear tomography from the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS) with the growth of structure from the WiggleZ Dark Energy Survey and the Six-degree-Field Galaxy Survey (6dFGS), producing the strongest existing joint constraints on the metric potentials that describe general theories of gravity. For scale-independent modifications to the metric potentials which evolve linearly with the effective dark energy density, we find present-day cosmological deviations in the Newtonian potential and curvature potential from the prediction of General Relativity to be (Delta Psi)/Psi = 0.05 \pm 0.25 and (Delta Phi)/Phi = -0.05 \pm 0.3 respectively (68 per cent CL)., Comment: 16 pages, 13 figures, accepted by MNRAS; v2: Figure 3 corrected, results unchanged

We present cosmological constraints from 2D weak gravitational lensing by the large-scale structure in the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS) which spans 154 square degrees in five optical bands. Using accurate photometric redshifts and measured shapes for 4.2 million galaxies between redshifts of 0.2 and 1.3, we compute the 2D cosmic shear correlation function over angular scales ranging between 0.8 and 350 arcmin. Using non-linear models of the dark-matter power spectrum, we constrain cosmological parameters by exploring the parameter space with Population Monte Carlo sampling. The best constraints from lensing alone are obtained for the small-scale density-fluctuations amplitude sigma_8 scaled with the total matter density Omega_m. For a flat LambdaCDM model we obtain sigma_8(Omega_m/0.27)^0.6 = 0.79+-0.03. We combine the CFHTLenS data with WMAP7, BOSS and an HST distance-ladder prior on the Hubble constant to get joint constraints. For a flat LambdaCDM model, we find Omega_m = 0.283+-0.010 and sigma_8 = 0.813+-0.014. In the case of a curved wCDM universe, we obtain Omega_m = 0.27+-0.03, sigma_8 = 0.83+-0.04, w_0 = -1.10+-0.15 and Omega_K = 0.006+0.006-0.004. We calculate the Bayesian evidence to compare flat and curved LambdaCDM and dark-energy CDM models. From the combination of all four probes, we find models with curvature to be at moderately disfavoured with respect to the flat case. A simple dark-energy model is indistinguishable from LambdaCDM. Our results therefore do not necessitate any deviations from the standard cosmological model., Comment: 21 pages, 13 figures, 10 tables. Accepted for publication in MNRAS

We present the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) that accurately determines a weak gravitational lensing signal from the full 154 square degrees of deep multi-colour data obtained by the CFHT Legacy Survey. Weak gravitational lensing by large-scale structure is widely recognised as one of the most powerful but technically challenging probes of cosmology. We outline the CFHTLenS analysis pipeline, describing how and why every step of the chain from the raw pixel data to the lensing shear and photometric redshift measurement has been revised and improved compared to previous analyses of a subset of the same data. We present a novel method to identify data which contributes a non-negligible contamination to our sample and quantify the required level of calibration for the survey. Through a series of cosmology-insensitive tests we demonstrate the robustness of the resulting cosmic shear signal, presenting a science-ready shear and photometric redshift catalogue for future exploitation., Comment: MNRAS in press (accepted 15th August 2012), 21 pages with 12 figures. See http://www.cfhtlens.org for information about the upcoming CFHTLenS full data release

We present a comparison of Fisher matrix forecasts for cosmological probes with Monte Carlo Markov Chain (MCMC) posterior likelihood estimation methods. We analyse the performance of future Dark Energy Task Force (DETF) stage-III and stage- IV dark-energy surveys using supernovae, baryon acoustic oscillations and weak lensing as probes. We concentrate in particular on the dark-energy equation of state parameters w0 and wa. For purely geometrical probes, and especially when marginalising over wa, we find considerable disagreement between the two methods, since in this case the Fisher matrix can not reproduce the highly non-elliptical shape of the likelihood function. More quantitatively, the Fisher method underestimates the marginalized errors for purely geometrical probes between 30%-70%. For cases including structure formation such as weak lensing, we find that the posterior probability contours from the Fisher matrix estimation are in good agreement with the MCMC contours and the forecasted errors only changing on the 5% level. We then explore non-linear transformations resulting in physically-motivated parameters and investigate whether these parameterisations exhibit a Gaussian behaviour. We conclude that for the purely geometrical probes and, more generally, in cases where it is not known whether the likelihood is close to Gaussian, the Fisher matrix is not the appropriate tool to produce reliable forecasts., Comment: 19 pages, 7 figures, table 2 updated

Extending previous studies, we derive generic predictions for lower order cumulants and their correlators for individual tomographic bins as well as between two different bins. We derive the corresponding one- and two-point joint probability distribution function for the tomographic convergence maps from different bins as a function of angular smoothing scale. The modelling of weak lensing statistics is obtained by adopting a detailed prescription for the underlying density contrast. In this paper we concentrate on the convergence field $\kappa$ and use top-hat filter; though the techniques presented can readily be extended to model the PDF of shear components or to include other windows such as the compensated filter. The functional form for the underlying PDF and bias is modelled in terms of the non-linear or the quasilinear form depending on the smoothing angular scale. Results from other semi-analytical models e.g. the lognormal distribution are also presented. Introducing a reduced convergence for individual bins, we are able to show that the tomographic PDFs and bias for each bin sample the same functional form of the underlying PDF of density contrast but with varying variance. The joint probability distribution of the convergence maps that correspond to two different tomographic bins can be constructed from individual tomographic PDF and bias. We study their dependence on cosmological parameters for source distributions corresponding to the realistic surveys such as LSST and DES. We briefly outline how photometric redshift information can be incorporated in our computation of cumulants, cumulant correlators and the PDFs. Connection of our results to the full 3D calculations is elucidated. Analytical results for inclusion of realistic noise and finite survey size are presented in detail., Comment: 19 pages, 10 Figures

We present the public release of the Bayesian sampling algorithm for cosmology, CosmoPMC (Cosmology Population Monte Carlo). CosmoPMC explores the parameter space of various cosmological probes, and also provides a robust estimate of the Bayesian evidence. CosmoPMC is based on an adaptive importance sampling method called Population Monte Carlo (PMC). Various cosmology likelihood modules are implemented, and new modules can be added easily. The importance-sampling algorithm is written in C, and fully parallelised using the Message Passing Interface (MPI). Due to very little overhead, the wall-clock time required for sampling scales approximately with the number of CPUs. The CosmoPMC package contains post-processing and plotting programs, and in addition a Monte-Carlo Markov chain (MCMC) algorithm. The sampling engine is implemented in the library pmclib, and can be used independently. The software is available for download at http://www.cosmopmc.info., Comment: CosmoPMC user's guide, version v1.2. Replaced v1.1

Context. Weak gravitational lensing is a powerful probe of large-scale structure and cosmology. Most commonly, second-order correlations of observed galaxy ellipticities are expressed as a projection of the matter power spectrum, corresponding to the lowest-order approximation between the projected and 3d power spectrum. Aims. The dominant lensing-only contribution beyond the zero-order approximation is the reduced shear, which takes into account not only lensing-induced distortions but also isotropic magnification of galaxy images. This involves an integral over the matter bispectrum. We provide a fast and general way to calculate this correction term. Methods. Using a model for the matter bispectrum, we fit elementary functions to the reduced-shear contribution and its derivatives with respect to cosmological parameters. The dependence on cosmology is encompassed in a Taylor-expansion around a fiducial model. Results. Within a region in parameter space comprising the WMAP7 68% error ellipsoid, the total reduced-shear power spectrum (shear plus fitted reduced-shear correction) is accurate to 1% (2%) for l<10^4 (l<2x10^5). This corresponds to a factor of four reduction of the bias compared to the case where no correction is used. This precision is necessary to match the accuracy of current non-linear power spectrum predictions from numerical simulations., Comment: 7 pages, 3 figures. A&A in press. Revised version with minor changes

We present a new technique to estimate the level of contamination between photometric redshift bins. If the true angular cross-correlation between redshift bins can be safely assumed to be zero, any measured cross-correlation is a result of contamination between the bins. We present the theory for an arbitrary number of redshift bins, and discuss in detail the case of two and three bins which can be easily solved analytically. We use mock catalogues constructed from the Millennium Simulation to test the method, showing that artificial contamination can be successfully recovered with our method. We find that degeneracies in the parameter space prohibit us from determining a unique solution for the contamination, though constraints are made which can be improved with larger data sets. We then apply the method to an observational galaxy survey: the deep component of the Canada-France-Hawaii Telescope Legacy Survey. We estimate the level of contamination between photometric redshift bins and demonstrate our ability to reconstruct both the true redshift distribution and the true average redshift of galaxies in each photometric bin., Comment: 14 pages, 12 figures, accepted for publication in MNRAS V2: Section 4.4 added. Significant additions to analysis in section 5.1

We use Bayesian model selection techniques to test extensions of the standard flat LambdaCDM paradigm. Dark-energy and curvature scenarios, and primordial perturbation models are considered. To that end, we calculate the Bayesian evidence in favour of each model using Population Monte Carlo (PMC), a new adaptive sampling technique which was recently applied in a cosmological context. The Bayesian evidence is immediately available from the PMC sample used for parameter estimation without further computational effort, and it comes with an associated error evaluation. Besides, it provides an unbiased estimator of the evidence after any fixed number of iterations and it is naturally parallelizable, in contrast with MCMC and nested sampling methods. By comparison with analytical predictions for simulated data, we show that our results obtained with PMC are reliable and robust. The variability in the evidence evaluation and the stability for various cases are estimated both from simulations and from data. For the cases we consider, the log-evidence is calculated with a precision of better than 0.08. Using a combined set of recent CMB, SNIa and BAO data, we find inconclusive evidence between flat LambdaCDM and simple dark-energy models. A curved Universe is moderately to strongly disfavoured with respect to a flat cosmology. Using physically well-motivated priors within the slow-roll approximation of inflation, we find a weak preference for a running spectral index. A Harrison-Zel'dovich spectrum is weakly disfavoured. With the current data, tensor modes are not detected; the large prior volume on the tensor-to-scalar ratio r results in moderate evidence in favour of r=0. [Abridged], Comment: 11 pages, 6 figures. Matches version accepted for publication by MNRAS

We present a tomographic cosmological weak lensing analysis of the HST COSMOS Survey. Applying our lensing-optimized data reduction, principal component interpolation for the ACS PSF, and improved modelling of charge-transfer inefficiency, we measure a lensing signal which is consistent with pure gravitational modes and no significant shape systematics. We carefully estimate the statistical uncertainty from simulated COSMOS-like fields obtained from ray-tracing through the Millennium Simulation. We test our pipeline on simulated space-based data, recalibrate non-linear power spectrum corrections using the ray-tracing, employ photometric redshifts to reduce potential contamination by intrinsic galaxy alignments, and marginalize over systematic uncertainties. We find that the lensing signal scales with redshift as expected from General Relativity for a concordance LCDM cosmology, including the full cross-correlations between different redshift bins. For a flat LCDM cosmology, we measure sigma_8(Omega_m/0.3)^0.51=0.75+-0.08 from lensing, in perfect agreement with WMAP-5, yielding joint constraints Omega_m=0.266+0.025-0.023, sigma_8=0.802+0.028-0.029 (all 68% conf.). Dropping the assumption of flatness and using HST Key Project and BBN priors only, we find a negative deceleration parameter q_0 at 94.3% conf. from the tomographic lensing analysis, providing independent evidence for the accelerated expansion of the Universe. For a flat wCDM cosmology and prior w in [-2,0], we obtain w<-0.41 (90% conf.). Our dark energy constraints are still relatively weak solely due to the limited area of COSMOS. However, they provide an important demonstration for the usefulness of tomographic weak lensing measurements from space. (abridged), Comment: 26 pages, 25 figures, matches version accepted for publication by Astronomy and Astrophysics

The decomposition of the cosmic shear field into E- and B-mode is an important diagnostic in weak gravitational lensing. However, commonly used techniques to perform this separation suffer from mode-mixing on very small or very large scales. We introduce a new E-/B-mode decomposition of the cosmic shear two-point correlation on a finite interval. This new statistic is optimised for cosmological applications, by maximising the signal-to-noise ratio (S/N) and a figure of merit (FoM) based on the Fisher matrix of the cosmological parameters Omega_m and sigma_8. We improve both S/N and FoM results substantially with respect to the recently introduced ring statistic, which also provides E-/B-mode separation on a finite angular range. The S/N (FoM) is larger by a factor of three (two) on angular scales between 1 and 220 arc minutes. In addition, it yields better results than for the aperture-mass dispersion ^2, with improvements of 20% (10%) for S/N (FoM). Our results depend on the survey parameters, most importantly on the covariance of the two-point shear correlation function. Although we assume parameters according to the CFHTLS-Wide survey, our method and optimisation scheme can be applied easily to any given survey settings and observing parameters. Arbitrary quantities, with respect to which the E-/B-mode filter is optimised, can be defined, therefore generalising the aim and context of the new shear statistic., Comment: 11 pages, 7 figures, 2 tables. MNRAS accepted. C-program freely available at http://www2.iap.fr/users/kilbinge/decomp_eb/

Supernova measurements have become a key ingredient in current determinations of cosmological parameters. These sources can however be used as standard candles only after correcting their apparent brightness for a number of effects. In this paper we discuss some limitations imposed by the formalism currently used for such corrections and investigate the impact on cosmological constraints. We show that color corrections are, in general, expected to be biased. In addition, color excesses which do not add a significant scatter to the observed SN brightnesses affect the value of cosmological parameters but leave the slope of the color-luminosity relation unchanged. We quantify these biases in the context of the redshift-dependent dust extinction suggested by the recent detection of intergalactic dust by Menard et al. (2009). Using a range of models for the opacity of the Universe as a function of redshift, we find that color-magnitude-stretch scaling relations are virtually insensitive to the presence of cosmic dust while cosmological parameters such as Omega_M and w are biased at the level of a few percent, i.e. offsets comparable to the current statistical errors. Future surveys will be able to limit the impact of intergalactic extinction by observing at larger wavelengths. In addition such datasets will provide direct detections of intergalactic dust by cross-correlating SN colors and the density of foreground galaxies, which can be used as a consistency check on the cosmic dust extinction correction. Alternatively, such biases could be avoided by correcting the colors of supernovae on an object-by-object basis with accurate photometry., Comment: 6 pages, 3 figures, submitted to MNRAS. Revised value in section 3.1

We present a Bayesian sampling algorithm called adaptive importance sampling or Population Monte Carlo (PMC), whose computational workload is easily parallelizable and thus has the potential to considerably reduce the wall-clock time required for sampling, along with providing other benefits. To assess the performance of the approach for cosmological problems, we use simulated and actual data consisting of CMB anisotropies, supernovae of type Ia, and weak cosmological lensing, and provide a comparison of results to those obtained using state-of-the-art Markov Chain Monte Carlo (MCMC). For both types of data sets, we find comparable parameter estimates for PMC and MCMC, with the advantage of a significantly lower computational time for PMC. In the case of WMAP5 data, for example, the wall-clock time reduces from several days for MCMC to a few hours using PMC on a cluster of processors. Other benefits of the PMC approach, along with potential difficulties in using the approach, are analysed and discussed., Comment: 17 pages, 11 figures