KiDS+VIKING-450 and DES-Y1 combined: Mitigating baryon feedback uncertainty with COSEBIs

We present cosmological constraints from a joint cosmic shear analysis of the Kilo-Degree Survey (KV450) and the Dark Energy Survey (DES-Y1), which were conducted using Complete Orthogonal Sets of E/B-Integrals (COSEBIs). With COSEBIs, we isolated any B-modes that have a non-cosmic shear origin and demonstrate the robustness of our cosmological E-mode analysis as no significant B-modes were detected. We highlight how COSEBIs are fairly insensitive to the amplitude of the non-linear matter power spectrum at high k-scales, mitigating the uncertain impact of baryon feedback in our analysis. COSEBIs, therefore, allowed us to utilise additional small-scale information, improving the DES-Y1 joint constraints on S8 = σ8(Ωm/0.3)0.5 and Ωm by 20%. By adopting a flat ΛCDM model we find S8 = 0.755−0.021+0.019, which is in 3.2σ tension with the Planck Legacy analysis of the cosmic microwave background

Intrinsic alignment boosting: Direct measurement of intrinsic alignments in cosmic shear data

Intrinsic alignments constitute the major astrophysical systematic for cosmological weak lensing surveys. We present a purely geometrical method with which one can study gravitational shear-intrinsic ellipticity correlations directly in weak lensing data. Linear combinations of second-order cosmic shear measures are constructed such that the intrinsic alignment signal is boosted while suppressing the contribution by gravitational lensing. We then assess the performance of a specific parametrisation of the weights entering these linear combinations for three representative survey models. Moreover a relation between this boosting technique and the intrinsic alignment removal via nulling is derived. For future all-sky weak lensing surveys with photometric redshift information the boosting technique yields statistical errors on model parameters of intrinsic alignments whose order of magnitude is compatible with current constraints determined from indirect measurements. Parameter biases due to a residual cosmic shear signal are negligible in case of quasi-spectroscopic redshifts and remain sub-dominant for typical values of the photometric redshift scatter. We find good agreement between the performance of the intrinsic alignment removal based on the boosting technique and standard nulling methods, possibly indicating a fundamental limit in the separation of lensing and intrinsic alignment signals.Comment: 15 pages, 7 figures; minor changes to match accepted version; published in Astronomy and Astrophysic

Calibration biases in measurements of weak lensing

As recently shown by Viola et al., the common (KSB) method for measuring weak gravitational shear creates a non-linear relation between the measured and the true shear of objects. We investigate here what effect such a non-linear calibration relation may have on cosmological parameter estimates from weak lensing if a simpler, linear calibration relation is assumed. We show that the non-linear relation introduces a bias in the shear-correlation amplitude and thus a bias in the cosmological parameters Omega_matter and sigma_8. Its direction and magnitude depends on whether the point-spread function is narrow or wide compared to the galaxy images from which the shear is measured. Substantial over- or underestimates of the cosmological parameters are equally possible, depending also on the variant of the KSB method. Our results show that for trustable cosmological-parameter estimates from measurements of weak lensing, one must verify that the method employed is free from ellipticity-dependent biases or monitor that the calibration relation inferred from simulations is applicable to the survey at hand.Comment: 5 pages, 3 figures, submitted to A&

Weak gravitational lensing with DEIMOS

We introduce a novel method for weak-lensing measurements, which is based on a mathematically exact deconvolution of the moments of the apparent brightness distribution of galaxies from the telescope's PSF. No assumptions on the shape of the galaxy or the PSF are made. The (de)convolution equations are exact for unweighted moments only, while in practice a compact weight function needs to be applied to the noisy images to ensure that the moment measurement yields significant results. We employ a Gaussian weight function, whose centroid and ellipticity are iteratively adjusted to match the corresponding quantities of the source. The change of the moments caused by the application of the weight function can then be corrected by considering higher-order weighted moments of the same source. Because of the form of the deconvolution equations, even an incomplete weighting correction leads to an excellent shear estimation if galaxies and PSF are measured with a weight function of identical size. We demonstrate the accuracy and capabilities of this new method in the context of weak gravitational lensing measurements with a set of specialized tests and show its competitive performance on the GREAT08 challenge data. A complete C++ implementation of the method can be requested from the authors.Comment: 7 pages, 3 figures, fixed typo in Eq. 1

The removal of shear-ellipticity correlations from the cosmic shear signal: Influence of photometric redshift errors on the nulling technique

Cosmic shear is regarded one of the most powerful probes to reveal the properties of dark matter and dark energy. To fully utilize its potential, one has to be able to control systematic effects down to below the level of the statistical parameter errors. Particularly worrisome in this respect is intrinsic alignment, causing considerable parameter biases via correlations between the intrinsic ellipticities of galaxies and the gravitational shear, which mimic lensing. In an earlier work we have proposed a nulling technique that downweights this systematic, only making use of its well-known redshift dependence. We assess the practicability of nulling, given realistic conditions on photometric redshift information. For several simplified intrinsic alignment models and a wide range of photometric redshift characteristics we calculate an average bias before and after nulling. Modifications of the technique are introduced to optimize the bias removal and minimize the information loss by nulling. We demonstrate that one of the presented versions is close to optimal in terms of bias removal, given high quality of photometric redshifts. For excellent photometric redshift information, i.e. at least 10 bins with a small dispersion, a negligible fraction of catastrophic outliers, and precise knowledge about the redshift distributions, one version of nulling is capable of reducing the shear-intrinsic ellipticity contamination by at least a factor of 100. Alternatively, we describe a robust nulling variant which suppresses the systematic signal by about 10 for a very broad range of photometric redshift configurations. Irrespective of the photometric redshift quality, a loss of statistical power is inherent to nulling, which amounts to a decrease of the order 50% in terms of our figure of merit.Comment: 26 pages, including 16 figures; minor changes to match accepted version; published in Astronomy and Astrophysic

Minimising the impact of scale-dependent galaxy bias on the joint cosmological analysis of large scale structures

We present a mitigation strategy to reduce the impact of non-linear galaxy bias on the joint ‘3 × 2pt’ cosmological analysis of weak lensing and galaxy surveys. The Ψ-statistics that we adopt are based on Complete Orthogonal Sets of E/B Integrals (COSEBIs). As such they are designed to minimize the contributions to the observable from the smallest physical scales where models are highly uncertain. We demonstrate that Ψ-statistics carry the same constraining power as the standard two-point galaxy clustering and galaxy-galaxy lensing statistics, but are significantly less sensitive to scale-dependent galaxy bias. Using two galaxy bias models, motivated by halo-model fits to data and simulations, we quantify the error in a standard 3 × 2pt analysis where constant galaxy bias is assumed. Even when adopting conservative angular scale cuts, that degrade the overall cosmological parameter constraints, we find of order 1σ biases for Stage III surveys on the cosmological parameter S8 = σ8(Ωm/0.3)α. This arises from a leakage of the smallest physical scales to all angular scales in the standard two-point correlation functions. In contrast, when analysing Ψ-statistics under the same approximation of constant galaxy bias, we show that the bias on the recovered value for S8 can be decreased by a factor of ∼2, with less conservative scale cuts. Given the challenges in determining accurate galaxy bias models in the highly non-linear regime, we argue that 3 × 2pt analyses should move towards new statistics that are less sensitive to the smallest physical scales

Cosmological Systematics Beyond Nuisance Parameters : Form Filling Functions

In the absence of any compelling physical model, cosmological systematics are often misrepresented as statistical effects and the approach of marginalising over extra nuisance systematic parameters is used to gauge the effect of the systematic. In this article we argue that such an approach is risky at best since the key choice of function can have a large effect on the resultant cosmological errors. As an alternative we present a functional form filling technique in which an unknown, residual, systematic is treated as such. Since the underlying function is unknown we evaluate the effect of every functional form allowed by the information available (either a hard boundary or some data). Using a simple toy model we introduce the formalism of functional form filling. We show that parameter errors can be dramatically affected by the choice of function in the case of marginalising over a systematic, but that in contrast the functional form filling approach is independent of the choice of basis set. We then apply the technique to cosmic shear shape measurement systematics and show that a shear calibration bias of |m(z)|< 0.001(1+z)^0.7 is required for a future all-sky photometric survey to yield unbiased cosmological parameter constraints to percent accuracy. A module associated with the work in this paper is available through the open source iCosmo code available at http://www.icosmo.org .Comment: 24 pages, 18 figures, accepted to MNRA

Very weak lensing in the CFHTLS Wide: Cosmology from cosmic shear in the linear regime

We present an exploration of weak lensing by large-scale structure in the linear regime, using the third-year (T0003) CFHTLS Wide data release. Our results place tight constraints on the scaling of the amplitude of the matter power spectrum sigma_8 with the matter density Omega_m. Spanning 57 square degrees to i'_AB = 24.5 over three independent fields, the unprecedented contiguous area of this survey permits high signal-to-noise measurements of two-point shear statistics from 1 arcmin to 4 degrees. Understanding systematic errors in our analysis is vital in interpreting the results. We therefore demonstrate the percent-level accuracy of our method using STEP simulations, an E/B-mode decomposition of the data, and the star-galaxy cross correlation function. We also present a thorough analysis of the galaxy redshift distribution using redshift data from the CFHTLS T0003 Deep fields that probe the same spatial regions as the Wide fields. We find sigma_8(Omega_m/0.25)^0.64 = 0.785+-0.043 using the aperture-mass statistic for the full range of angular scales for an assumed flat cosmology, in excellent agreement with WMAP3 constraints. The largest physical scale probed by our analysis is 85 Mpc, assuming a mean redshift of lenses of 0.5 and a LCDM cosmology. This allows for the first time to constrain cosmology using only cosmic shear measurements in the linear regime. Using only angular scales theta> 85 arcmin, we find sigma_8(Omega_m/0.25)_lin^0.53 = 0.837+-0.084, which agree with the results from our full analysis. Combining our results with data from WMAP3, we find Omega_m=0.248+-0.019 and sigma_8 = 0.771+-0.029.Comment: 23 pages, 16 figures (A&A accepted

Enhancing the cosmic shear power spectrum

Applying a transformation to a non-Gaussian field can enhance the information content of the resulting power spectrum, by reducing the correlations between Fourier modes. In the context of weak gravitational lensing, it has been shown that this gain in information content is significantly compromised by the presence of shape noise. We apply clipping to mock convergence fields, a technique which is known to be robust in the presence of noise and has been successfully applied to galaxy number density fields. When analysed in isolation the resulting convergence power spectrum returns degraded constraints on cosmological parameters. However, substantial gains can be achieved by performing a combined analysis of the power spectra derived from both the original and transformed fields. Even in the presence of realistic levels of shape noise, we demonstrate that this approach is capable of reducing the area of likelihood contours within the Ωm − σ8 plane by more than a factor of 3