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In this paper we show how response function corrections to shear measurements (e.g. as required by Metacalibration) propagate into cosmic shear power spectra. We investigate a 2-sphere pixel (also known as HEALpixel') correction and a forward-modelling approach using simple Gaussian simulations. In the 2-sphere pixel-correction approach we find a free parameter that is the tolerated condition number of the local response matrices: if this is too large then this can cause an amplification of the shot noise power spectrum, if too small it can lead to a loss of area (and a possible selection bias). In contrast by forward-modelling the power spectrum this choice can be avoided. This also applies to map-based inference methods using shear-response calibrated maps., Comment: 4 pages, 1 figure, submitted to Open Journal of Astrophysics

In this paper we revisit potential biases in cosmic shear power spectra caused by bias terms that multiply up to quadratic powers of the shear. Expanding the multiplicative bias field as a series of independent spin-$s$ fields we find terms $m_s$ that multiply integer and half-integer powers of the shear. We propagate these biases into shape measurement statistics and the cosmic shear power spectrum. We find that such biases can be measured by performing regression on calibration data. We find that for integer powers of shear the impact of quadratic order terms on the power spectrum is an additional bispectrum dependency; ignoring quadratic terms can lead to biases in cosmological parameters of up to $2(m_2+m_{-2}-m_6)0.4\sigma$ for Stage-IV dark energy experiments, but that the susceptibility to them can be decreased by using methods to remove small-scale sensitivity. We also find, for half-integer powers of the shear that, for a Stage-IV experiment, biases are required to be known to better than approximately $\sigma[m^R_0+15(m^R_1+m^R_3)+0.1(m^R_{-1}+m^R_5)]\leq 0.01$. In future, Stage-IV dark energy experiments should seek to measure and minimise such all such bias terms., Comment: Submitted to the Open Journal of Astrophysics. Analysis extended in second version

In this paper we revisit potential biases in cosmic shear power spectra caused by bias terms that multiply up to quadratic powers of the shear. Expanding the multiplicative bias field as a series of independent spin-$s$ fields we find terms $m_s$ that multiply integer and half-integer powers of the shear. We propagate these biases into shape measurement statistics and the cosmic shear power spectrum. We find that such biases can be measured by performing regression on calibration data. We find that for integer powers of shear the impact of quadratic order terms on the power spectrum is an additional bispectrum dependency; ignoring quadratic terms can lead to biases in cosmological parameters of up to $2(m_2+m_{-2}-m_6)0.4\sigma$ for Stage-IV dark energy experiments, but that the susceptibility to them can be decreased by using methods to remove small-scale sensitivity. We also find, for half-integer powers of the shear that, for a Stage-IV experiment, biases are required to be known to better than approximately $\sigma[m_0+15(m_1+m_3)+0.1(m_{-1}+m_5)]\leq 0.01$. In future, Stage-IV dark energy experiments should seek to measure and minimise such all such bias terms., Comment: Accepted to the Open Journal of Astrophysics

In this paper we address the challenge of extracting maps of spatially varying unknown additive biases from cosmic shear data. This is done by exploiting the isotropy of the cosmic shear field, and the anisotropy of a typical additive bias field, using an autocorrelation discrepancy map; which identifies significant non-Gaussian components of the map. We test this approach using simulations and find that the autocorrelation discrepancy map produces spatially varying features that are indicative of the additive bias field both in amplitude and spatial variation. We then apply this to the Dark Energy Survey Year 1 data, and find evidence for spatially varying additive biases of at most 0.002 on large-scales. The method can be used to empirically inform modelling of the spatially varying additive bias field in any cosmological parameter inference, and can act as a validation test for cosmic shear surveys., Comment: Accepted to the Open Journal of Astrophysics

We introduce a novel statistic to probe the statistics of phases of Fourier modes in two-dimensions (2D) for weak lensing convergence field $\kappa$. This statistic contains completely independent information compared to that contained in observed power spectrum. We compare our results against state-of-the-art numerical simulations as a function of source redshift and find good agreement with theoretical predictions. We show that our estimator can achieve better signal-to-noise compared to the commonly employed statistics known as the line correlation function (LCF). Being a two-point statistics, our estimator is also easy to implement in the presence of complicated noise and mask, and can also be generalised to higher-order. While applying this estimator for the study of lensed CMB maps, we show that it is important to include post-Born corrections in the study of statistics of phase., Comment: 18 pages, 7 figures

In this paper we address the challenge of extracting maps of spatially varying unknown additive biases from cosmic shear data. This is done by exploiting the isotropy of the cosmic shear field, and the anisotropy of a typical additive bias field, using an autocorrelation discrepancy map; which identifies significant non-Gaussian components of the map. We test this approach using simulations and find that the autocorrelation discrepancy map produces spatially varying features that are indicative of the additive bias field both in amplitude and spatial variation. We then apply this to the Dark Energy Survey Year 1 data, and find evidence for spatially varying additive biases of at most 0.002 on large-scales. The method can be used to empirically inform modelling of the spatially varying additive bias field in any cosmological parameter inference, and can act as a validation test for cosmic shear surveys., Comment: Accepted to the Open Journal of Astrophysics

We introduce a novel statistic to probe the statistics of phases of Fourier modes in two-dimensions (2D) for weak lensing convergence field $\kappa$. This statistic contains completely independent information compared to that contained in observed power spectrum. We compare our results against state-of-the-art numerical simulations as a function of source redshift and find good agreement with theoretical predictions. We show that our estimator can achieve better signal-to-noise compared to the commonly employed statistics known as the line correlation function (LCF). Being a two-point statistics, our estimator is also easy to implement in the presence of complicated noise and mask, and can also be generalised to higher-order. While applying this estimator for the study of lensed CMB maps, we show that it is important to include post-Born corrections in the study of statistics of phase., Comment: 18 pages, 7 figures

We provide a systematic study of the position-dependent correlation function in weak lensing convergence maps and its relation to the squeezed limit of the three-point correlation function (3PCF) using state-of-the-art numerical simulations. We relate the position-dependent correlation function to its harmonic counterpart, i.e., the position-dependent power spectrum or equivalently the integrated bispectrum. We use a recently proposed improved fitting function, BiHalofit, for the bispectrum to compute the theoretical predictions as a function of source redshifts. In addition to low redshift results ($z_s=1.0-2.0$), we also provide results for maps inferred from lensing of the cosmic microwave background, i.e., $z_s=1100$. We include a {\em Euclid}-type realistic survey mask and noise. In agreement with the recent studies on the position-dependent power spectrum, we find that the results from simulations are consistent with the theoretical expectations when appropriate corrections are included. Performing a rough estimate, we find that the (S/N) for the detection of the position-dependent correlation function from {\em Euclid}-type mask with $f_{sky}=0.35$, can range between $6-12$ depending on the value of the intrinsic ellipticity distribution parameter $\sigma_{\epsilon} = 0.3-1.0$. For reconstructed $\kappa$ maps using an ideal CMB survey the (S/N) $\approx 1.8$. We also found that a $10\%$ deviation in $\sigma_8$ can be detected using IB for the optimistic case of $\sigma_\epsilon=0.3$ with a (S/N) $\approx 5$. The (S/N) for such detection in case of $\Omega_M$ is lower., Comment: 7 pages, 7 figures (PRD in press)

We introduce the skew-spectrum statistic for weak lensing convergence $\kappa$ maps and test it against state-of-the-art high-resolution all-sky numerical simulations. We perform the analysis as a function of source redshift and smoothing angular scale for individual tomographic bins. We also analyse the cross-correlation between different tomographic bins. We compare the numerical results to fitting-functions used to model the bispectrum of the underlying density field as a function of redshift and scale. We derive a closed form expression for the skew-spectrum for gravity-induced secondary non-Gaussianity. We also compute the skew-spectrum for the projected $\kappa$ inferred from Cosmic Microwave Background (CMB) studies. As opposed to the low redshift case we find the post-Born corrections to be important in the modelling of the skew-spectrum for such studies. We show how the presence of a mask and noise can be incorporated in the estimation of a skew-spectrum., Comment: 16 pages, 11 figures

Upcoming surveys will map the growth of large-scale structure with unprecented precision, improving our understanding of the dark sector of the Universe. Unfortunately, much of the cosmological information is encoded by the small scales, where the clustering of dark matter and the effects of astrophysical feedback processes are not fully understood. This can bias the estimates of cosmological parameters, which we study here for a joint analysis of mock Euclid cosmic shear and Planck cosmic microwave background data. We use different implementations for the modelling of the signal on small scales and find that they result in significantly different predictions. Moreover, the different nonlinear corrections lead to biased parameter estimates, especially when the analysis is extended into the highly nonlinear regime, with both the Hubble constant, $H_0$, and the clustering amplitude, $\sigma_8$, affected the most. Improvements in the modelling of nonlinear scales will therefore be needed if we are to resolve the current tension with more and better data. For a given prescription for the nonlinear power spectrum, using different corrections for baryon physics does not significantly impact the precision of Euclid, but neglecting these correction does lead to large biases in the cosmological parameters. In order to extract precise and unbiased constraints on cosmological parameters from Euclid cosmic shear data, it is therefore essential to improve the accuracy of the recipes that account for nonlinear structure formation, as well as the modelling of the impact of astrophysical processes that redistribute the baryons., Comment: 18 pages, 6 figures. Prepared for submission to Astronomy & Astrophysics

In this paper we derive a full expression for the propagation of weak lensing shape measurement biases into cosmic shear power spectra including the effect of missing data. We show using simulations that terms higher than first order in bias parameters can be ignored and the impact of biases can be captured by terms dependent only on the mean of the multiplicative bias field. We identify that the B-mode power contains information on the multiplicative bias. We find that without priors on the residual multiplicative bias $\delta m$ and stochastic ellipticity variance $\sigma_e$ that constraints on the amplitude of the cosmic shear power spectrum are completely degenerate, and that when applying priors the constrained amplitude $A$ is slightly biased low via a classic marginalisation paradox. Using all-sky Gaussian random field simulations we find that the combination of $(1+2\delta m)A$ is unbiased for a joint EE and BB power spectrum likelihood if the error and mean (precision and accuracy) of the stochastic ellipticity variance is known to better than $\sigma(\sigma_e)\leq 0.05$ and $\Delta\sigma_e\leq 0.01$, or the multiplicative bias is known to better than $\sigma(m)\leq 0.07$ and $\Delta m\leq 0.01$., Comment: 12 pages, accepted to the Open Journal of Astrophysics, comments welcome

We study the morphology of convergence maps by perturbatively reconstructing their Minkowski Functionals (MFs). We present a systematics study using a set of three generalised skew-spectra as a function of source redshift and smoothing angular scale. Using an approach based on pseudo-$S_{\ell}$s (PSL) we show how these spectra will allow reconstruction of MFs in the presence of an arbitrary mask and inhomogeneous noise in an unbiased way. Our theoretical predictions are based on a recently introduced fitting function to the bispectrum. We compare our results against state-of-the art numerical simulations and find an excellent agreement. The reconstruction can be carried out in a controlled manner as a function of angular harmonics $\ell$ and source redshift $z_s$ which allows for a greater handle on any possible sources of non-Gaussianity. Our method has the advantage of estimating the topology of convergence maps directly using shear data. We also study weak lensing convergence maps inferred from Cosmic Microwave Background (CMB) observations; and we find that, though less significant at low redshift, the post-Born corrections play an important role in any modelling of the non-Gaussianity of convergence maps at higher redshift. We also study the cross-correlations of estimates from different tomographic bins., Comment: 16 pages, 12 figures

Forthcoming large photometric surveys for cosmology require precise and accurate photometric redshift (photo-z) measurements for the success of their main science objectives. However, to date, no method has been able to produce photo-$z$s at the required accuracy using only the broad-band photometry that those surveys will provide. An assessment of the strengths and weaknesses of current methods is a crucial step in the eventual development of an approach to meet this challenge. We report on the performance of 13 photometric redshift code single value redshift estimates and redshift probability distributions (PDZs) on a common set of data, focusing particularly on the 0.2--2.6 redshift range that the Euclid mission will probe. We design a challenge using emulated Euclid data drawn from three photometric surveys of the COSMOS field. The data are divided into two samples: one calibration sample for which photometry and redshifts are provided to the participants; and the validation sample, containing only the photometry, to ensure a blinded test of the methods. Participants were invited to provide a redshift single value estimate and a PDZ for each source in the validation sample, along with a rejection flag that indicates sources they consider unfit for use in cosmological analyses. The performance of each method is assessed through a set of informative metrics, using cross-matched spectroscopic and highly-accurate photometric redshifts as the ground truth. We show that the rejection criteria set by participants are efficient in removing strong outliers, sources for which the photo-z deviates by more than 0.15(1+z) from the spectroscopic-redshift (spec-z). We also show that, while all methods are able to provide reliable single value estimates, several machine-learning methods do not manage to produce useful PDZs. [abridged], Comment: Accepted in A&A, 25 pages, 13 figures, 7 tables

In metric theories of gravity with photon number conservation, the luminosity and angular diameter distances are related via the Etherington relation, also known as the distance-duality relation (DDR). A violation of this relation would rule out the standard cosmological paradigm and point at the presence of new physics. We quantify the ability of Euclid, in combination with contemporary surveys, to improve the current constraints on deviations from the DDR in the redshift range $0

We introduce the skew-spectrum statistic for weak lensing convergence $\kappa$ maps and test it against state-of-the-art high-resolution all-sky numerical simulations. We perform the analysis as a function of source redshift and smoothing angular scale for individual tomographic bins. We also analyse the cross-correlation between different tomographic bins. We compare the numerical results to fitting-functions used to model the bispectrum of the underlying density field as a function of redshift and scale. We derive a closed form expression for the skew-spectrum for gravity-induced secondary non-Gaussianity. We also compute the skew-spectrum for the projected $\kappa$ inferred from Cosmic Microwave Background (CMB) studies. As opposed to the low redshift case we find the post-Born corrections to be important in the modelling of the skew-spectrum for such studies. We show how the presence of a mask and noise can be incorporated in the estimation of a skew-spectrum., Comment: 16 pages, 11 figures

Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed. In this work, we evaluate the impact of the reduced shear approximation and magnification bias, on the information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological parameters that can no longer be neglected. A separate bias arises from the statistics of shear being altered by the preferential selection of galaxies and the dilution of their surface densities, in high-magnification regions. The corrections for these systematic effects take similar forms, allowing them to be treated together. We calculated the impact of neglecting these effects on the cosmological parameters that would be determined from Euclid, using cosmic shear tomography. To do so, we employed the Fisher matrix formalism, and included the impact of the super-sample covariance. We also demonstrate how the reduced shear correction can be calculated using a lognormal field forward modelling approach. These effects cause significant biases in Omega_m, sigma_8, n_s, Omega_DE, w_0, and w_a of -0.53 sigma, 0.43 sigma, -0.34 sigma, 1.36 sigma, -0.68 sigma, and 1.21 sigma, respectively. We then show that these lensing biases interact with another systematic: the intrinsic alignment of galaxies. Accordingly, we develop the formalism for an intrinsic alignment-enhanced lensing bias correction. Applying this to Euclid, we find that the additional terms introduced by this correction are sub-dominant., Comment: 16 pages, 6 figures, submitted to Astronomy & Astrophysics on 16/12/2019, accepted on 04/03/2020. SSC Fisher procedure corrected

Our aim is to quantify the impact of systematic effects on the inference of cosmological parameters from cosmic shear. We present an end-to-end approach that introduces sources of bias in a modelled weak lensing survey on a galaxy-by-galaxy level. Residual biases are propagated through a pipeline from galaxy properties (one end) through to cosmic shear power spectra and cosmological parameter estimates (the other end), to quantify how imperfect knowledge of the pipeline changes the maximum likelihood values of dark energy parameters. We quantify the impact of an imperfect correction for charge transfer inefficiency (CTI) and modelling uncertainties of the point spread function (PSF) for Euclid, and find that the biases introduced can be corrected to acceptable levels., Comment: 18 pages. Submitted to A&A. Comments Welcome

Recent studies have demonstrated that {\em secondary} non-Gaussianity induced by gravity will be detected with a high signal-to-noise (S/N) by future and even by on-going weak lensing surveys. One way to characterise such non-Gaussianity is through the detection of a non-zero three-point correlation function of the lensing convergence field, or of its harmonic transform, the bispectrum. A recent study analysed the properties of the squeezed configuration of the bispectrum, when two wavenumbers are much larger than the third one. We extend this work by estimating the amplitude of the (reduced) bispectrum in four generic configurations, i.e., {\em squeezed, equilateral, isosceles} and {\em folded}, and for four different source redshifts $z_s=0.5,1.0,1.5,2.0$, by using an ensemble of all-sky high-resolution simulations. We compare these results against theoretical predictions. We find that, while the theoretical expectations based on widely used fitting functions can predict the general trends of the reduced bispectra, a more accurate theoretical modelling will be required to analyse the next generation of all-sky weak lensing surveys. The disagreement is particularly pronounced in the squeezed limit., Comment: 12 pages, 2 figures

Galaxy mergers and interactions are an integral part of our basic understanding of how galaxies grow and evolve over time. However, the effect that galaxy mergers have on star formation rates (SFR) is contested, with observations of galaxy mergers showing reduced, enhanced and highly enhanced star formation. We aim to determine the effect of galaxy mergers on the SFR of galaxies using statistically large samples of galaxies, totalling over 200\,000, over a large redshift range, 0.0 to 4.0. We train and use convolutional neural networks to create binary merger identifications (merger or non-merger) in the SDSS, KiDS and CANDELS imaging surveys. We then compare the galaxy main sequence subtracted SFR of the merging and non-merging galaxies to determine what effect, if any, a galaxy merger has on SFR. We find that the SFR of merging galaxies are not significantly different from the SFR of non-merging systems. The changes in the average SFR seen in the star forming population when a galaxy is merging are small, of the order of a factor of 1.2. However, the higher the SFR above the galaxy main sequence, the higher the fraction of galaxy mergers. Galaxy mergers have little effect on the SFR of the majority of merging galaxies compared to the non-merging galaxies. The typical change in SFR is less than 0.1~dex in either direction. Larger changes in SFR can be seen but are less common. The increase in merger fraction as the distance above the galaxy main sequence increases demonstrates that galaxy mergers can induce starbursts., Comment: 20 pages, 17 figures, 6 tables, 3 appendices, accepted for publication in A&A

Context. Future weak lensing surveys, such as the Euclid mission, will attempt to measure the shapes of billions of galaxies in order to derive cosmological information. These surveys will attain very low levels of statistical error, and systematic errors must be extremely well controlled. In particular, the point spread function (PSF) must be estimated using stars in the field, and recovered with high accuracy. Aims. The aims of this paper are twofold. Firstly, we took steps toward a nonparametric method to address the issue of recovering the PSF field, namely that of finding the correct PSF at the position of any galaxy in the field, applicable to Euclid. Our approach relies solely on the data, as opposed to parametric methods that make use of our knowledge of the instrument. Secondly, we studied the impact of imperfect PSF models on the shape measurement of galaxies themselves, and whether common assumptions about this impact hold true in an Euclid scenario. Methods. We extended the recently proposed resolved components analysis approach, which performs super-resolution on a field of under-sampled observations of a spatially varying, image-valued function. We added a spatial interpolation component to the method, making it a true 2-dimensional PSF model. We compared our approach to PSFEx, then quantified the impact of PSF recovery errors on galaxy shape measurements through image simulations. Results. Our approach yields an improvement over PSFEx in terms of the PSF model and on observed galaxy shape errors, though it is at present far from reaching the required Euclid accuracy. We also find that the usual formalism used for the propagation of PSF model errors to weak lensing quantities no longer holds in the case of an Euclid-like PSF. In particular, different shape measurement approaches can react differently to the same PSF modeling errors., Comment: 19 pages, 19 figures. This version matches that published in A&A

In this paper we derive a full expression for the propagation of multiplicative and additive shape measurement biases into the cosmic shear power spectrum. In doing so we identify several new terms that are associated with selection effects, as well as cross-correlation terms between the multiplicative and additive biases and the shear field. The computation of the resulting bias in the shear power spectrum scales as the fifth power of the maximum multipole considered. Consequently the calculation is unfeasible for large l-modes, and the only tractable way to assess the full impact of shape measurement biases on cosmic shear power spectrum is through forward modelling of the effects. To linear order in bias parameters the shear power spectrum is only affected by the mean of the multiplicative bias field over a survey and the cross correlation between the additive bias field and the shear field. If the mean multiplicative bias is zero then second order convolutive terms are expected to be orders of magnitude smaller., Comment: 10 pages, accepted to the Open Journal of Astrophysics

In this paper we address the problem of finding optimal cosmic shear tomographic bins. We generalise the definition of a cosmic shear tomographic bin to be a set of commonly labelled voxels in photometric colour space; rather than bins defined directly in redshift. We explore this approach by using a self-organising map to define the multi-dimensional colour space, and a we define a 'label space' of connected regions on the self-organising map using overlapping elliptical disks. This allows us to then find optimal labelling schemes by searching the label space. We use a metric that is the signal-to-noise ratio of a dark energy equation of state measurement, and in this case we find that for up to five tomographic bins the optimal colour-space labelling is an approximation of an equally-spaced binning in redshift; that is in all cases the best configuration. We also show that such a redefinition is more robust to photometric redshift outliers than a standard tomographic bin selection., Comment: 10 pages, submitted to PRD, comments welcome

Context. Future weak lensing surveys, such as the Euclid mission, will attempt to measure the shapes of billions of galaxies in order to derive cosmological information. These surveys will attain very low levels of statistical error, and systematic errors must be extremely well controlled. In particular, the point spread function (PSF) must be estimated using stars in the field, and recovered with high accuracy. Aims. The aims of this paper are twofold. Firstly, we took steps toward a nonparametric method to address the issue of recovering the PSF field, namely that of finding the correct PSF at the position of any galaxy in the field, applicable to Euclid. Our approach relies solely on the data, as opposed to parametric methods that make use of our knowledge of the instrument. Secondly, we studied the impact of imperfect PSF models on the shape measurement of galaxies themselves, and whether common assumptions about this impact hold true in an Euclid scenario. Methods. We extended the recently proposed resolved components analysis approach, which performs super-resolution on a field of under-sampled observations of a spatially varying, image-valued function. We added a spatial interpolation component to the method, making it a true 2-dimensional PSF model. We compared our approach to PSFEx, then quantified the impact of PSF recovery errors on galaxy shape measurements through image simulations. Results. Our approach yields an improvement over PSFEx in terms of the PSF model and on observed galaxy shape errors, though it is at present far from reaching the required Euclid accuracy. We also find that the usual formalism used for the propagation of PSF model errors to weak lensing quantities no longer holds in the case of an Euclid-like PSF. In particular, different shape measurement approaches can react differently to the same PSF modeling errors., Comment: 19 pages, 19 figures. This version matches that published in A&A

In this paper we derive a full expression for the propagation of multiplicative and additive shape measurement biases into the cosmic shear power spectrum. In doing so we identify several new terms that are associated with selection effects, as well as cross-correlation terms between the multiplicative and additive biases and the shear field. The computation of the resulting bias in the shear power spectrum scales as the fifth power of the maximum multipole considered. Consequently the calculation is unfeasible for large l-modes, and the only tractable way to assess the full impact of shape measurement biases on cosmic shear power spectrum is through forward modelling of the effects. To linear order in bias parameters the shear power spectrum is only affected by the mean of the multiplicative bias field over a survey and the cross correlation between the additive bias field and the shear field. If the mean multiplicative bias is zero then second order convolutive terms are expected to be orders of magnitude smaller., Comment: 10 pages, accepted to the Open Journal of Astrophysics

In this paper we address the problem of finding optimal cosmic shear tomographic bins. We generalise the definition of a cosmic shear tomographic bin to be a set of commonly labelled voxels in photometric colour space; rather than bins defined directly in redshift. We explore this approach by using a self-organising map to define the multi-dimensional colour space, and a we define a 'label space' of connected regions on the self-organising map using overlapping elliptical disks. This allows us to then find optimal labelling schemes by searching the label space. We use a metric that is the signal-to-noise ratio of a dark energy equation of state measurement, and in this case we find that for up to five tomographic bins the optimal colour-space labelling is an approximation of an equally-spaced binning in redshift; that is in all cases the best configuration. We also show that such a redefinition is more robust to photometric redshift outliers than a standard tomographic bin selection., Comment: 10 pages, submitted to PRD, comments welcome

Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed. In this work, we evaluate the impact of the reduced shear approximation and magnification bias, on the information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological parameters that can no longer be neglected. A separate bias arises from the statistics of shear being altered by the preferential selection of galaxies and the dilution of their surface densities, in high-magnification regions. The corrections for these systematic effects take similar forms, allowing them to be treated together. We calculated the impact of neglecting these effects on the cosmological parameters that would be determined from Euclid, using cosmic shear tomography. To do so, we employed the Fisher matrix formalism, and included the impact of the super-sample covariance. We also demonstrate how the reduced shear correction can be calculated using a lognormal field forward modelling approach. These effects cause significant biases in Omega_m, sigma_8, n_s, Omega_DE, w_0, and w_a of -0.53 sigma, 0.43 sigma, -0.34 sigma, 1.36 sigma, -0.68 sigma, and 1.21 sigma, respectively. We then show that these lensing biases interact with another systematic: the intrinsic alignment of galaxies. Accordingly, we develop the formalism for an intrinsic alignment-enhanced lensing bias correction. Applying this to Euclid, we find that the additional terms introduced by this correction are sub-dominant., Comment: 16 pages, 6 figures, submitted to Astronomy & Astrophysics on 16/12/2019, accepted on 04/03/2020. SSC Fisher procedure corrected

Our aim is to quantify the impact of systematic effects on the inference of cosmological parameters from cosmic shear. We present an end-to-end approach that introduces sources of bias in a modelled weak lensing survey on a galaxy-by-galaxy level. Residual biases are propagated through a pipeline from galaxy properties (one end) through to cosmic shear power spectra and cosmological parameter estimates (the other end), to quantify how imperfect knowledge of the pipeline changes the maximum likelihood values of dark energy parameters. We quantify the impact of an imperfect correction for charge transfer inefficiency (CTI) and modelling uncertainties of the point spread function (PSF) for Euclid, and find that the biases introduced can be corrected to acceptable levels., Comment: 18 pages. Submitted to A&A. Comments Welcome

Recent studies have demonstrated that {\em secondary} non-Gaussianity induced by gravity will be detected with a high signal-to-noise (S/N) by future and even by on-going weak lensing surveys. One way to characterise such non-Gaussianity is through the detection of a non-zero three-point correlation function of the lensing convergence field, or of its harmonic transform, the bispectrum. A recent study analysed the properties of the squeezed configuration of the bispectrum, when two wavenumbers are much larger than the third one. We extend this work by estimating the amplitude of the (reduced) bispectrum in four generic configurations, i.e., {\em squeezed, equilateral, isosceles} and {\em folded}, and for four different source redshifts $z_s=0.5,1.0,1.5,2.0$, by using an ensemble of all-sky high-resolution simulations. We compare these results against theoretical predictions. We find that, while the theoretical expectations based on widely used fitting functions can predict the general trends of the reduced bispectra, a more accurate theoretical modelling will be required to analyse the next generation of all-sky weak lensing surveys. The disagreement is particularly pronounced in the squeezed limit., Comment: 12 pages, 2 figures

Galaxy mergers and interactions are an integral part of our basic understanding of how galaxies grow and evolve over time. However, the effect that galaxy mergers have on star formation rates (SFR) is contested, with observations of galaxy mergers showing reduced, enhanced and highly enhanced star formation. We aim to determine the effect of galaxy mergers on the SFR of galaxies using statistically large samples of galaxies, totalling over 200\,000, over a large redshift range, 0.0 to 4.0. We train and use convolutional neural networks to create binary merger identifications (merger or non-merger) in the SDSS, KiDS and CANDELS imaging surveys. We then compare the galaxy main sequence subtracted SFR of the merging and non-merging galaxies to determine what effect, if any, a galaxy merger has on SFR. We find that the SFR of merging galaxies are not significantly different from the SFR of non-merging systems. The changes in the average SFR seen in the star forming population when a galaxy is merging are small, of the order of a factor of 1.2. However, the higher the SFR above the galaxy main sequence, the higher the fraction of galaxy mergers. Galaxy mergers have little effect on the SFR of the majority of merging galaxies compared to the non-merging galaxies. The typical change in SFR is less than 0.1~dex in either direction. Larger changes in SFR can be seen but are less common. The increase in merger fraction as the distance above the galaxy main sequence increases demonstrates that galaxy mergers can induce starbursts., Comment: 20 pages, 17 figures, 6 tables, 3 appendices, accepted for publication in A&A

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission., QC 20180521

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

Given a standard model to test, an experiment can be designed to (i) measure the standard model parameters, (ii) extend the standard model or (iii) look for evidence of deviations from the standard model. To measure (or extend) the standard model, the Fisher matrix is widely used in cosmology to predict expected parameter errors for future surveys under Gaussian assumptions. In this paper, we present a framework that can be used to design experiments that will maximize the chance of finding a deviation from the standard model. Using a simple illustrative example, discussed in Appendix A, we show that the optimal experimental configuration can depend dramatically on the optimization approach chosen. We also show some simple cosmology calculations, where we study baryonic acoustic oscillation and supernovae surveys. In doing so, we also show how external data, such as the positions of the cosmic microwave background peak measured by Wilkinson Microwave Anisotropy Probe, and theory priors can be included in the analysis. In the cosmological cases that we have studied (Dark Energy Task Force Stage III), we find that the three optimization approaches yield similar results, which is reassuring and indicates that the choice of optimal experiment is fairly robust at this level. However, this may not be the case as we move to more ambitious future surveys

Within the context of constraining an expansion of the dark energy equation of state w(z), we show that the eigendecomposition of Fisher matrices is sensitive to both the maximum order of the expansion and the basis set choice. We investigate the Fisher matrix formalism in the case that a particular function is expanded in some basis set. As an example we show results for an all-sky weak lensing tomographic experiment. We show that the set of eigenfunctions is not unique and that the best constrained functions are only reproduced accurately at very higher order N≳ 100, a top-hat basis set requires an even higher order. We show that the common approach used for finding the marginalized eigenfunction errors is sensitive to the choice of non-w(z) parameters and priors. The eigendecomposition of Fisher matrices is a potentially useful tool that can be used to determine the predicted accuracy with which an experiment could constrain w(z). It also allows for the reconstruction of the redshift sensitivity of the experiment to changes in w(z). However, the technique is sensitive to both the order and the basis set choice. Publicly available code is available as part of icosmo at http://www.icosmo.org

We present weak lensing and X-ray analysis of 12 low-mass clusters from the Canada-France-Hawaii Telescope Lensing Survey and XMM-CFHTLS surveys. We combine these systems with high-mass systems from Canadian Cluster Comparison Project and low-mass systems from Cosmic Evolution Survey to obtain a sample of 70 systems, spanning over two orders of magnitude in mass. We measure core-excised LX-TX, M-LX and M-TX scaling relations and include corrections for observational biases. By providing fully bias-corrected relations, we give the current limitations for LX and TX as cluster mass proxies. We demonstrate that TX benefits from a significantly lower intrinsic scatter at fixed mass than LX. By studying the residuals of the bias-corrected relations, we show for the first time using weak lensing masses that galaxy groups seem more luminous and warmer for their mass than clusters. This implies a steepening of the M-LX and M-TX relations at low masses. We verify the inferred steepening using a different high-mass sample from the literature and show that variance between samples is the dominant effect leading to discrepant scaling relations. We divide our sample into subsamples of merging and relaxed systems, and find that mergers may have enhanced scatter in lensing measurements, most likely due to stronger triaxiality and more substructure. For the LX-TX relation, which is unaffected by lensing measurements, we find the opposite trend in scatter. We also explore the effects of X-ray cross-calibration and find that Chandra calibration leads to flatter LX-TX and M-TX relations than XMM-Newton

In this paper, we present results from the weak-lensing shape measurement GRavitational lEnsing Accuracy Testing 2010 (GREAT10) Galaxy Challenge. This marks an order of magnitude step change in the level of scrutiny employed in weak-lensing shape measurement analysis. We provide descriptions of each method tested and include 10 evaluation metrics over 24 simulation branches. GREAT10 was the first shape measurement challenge to include variable fields; both the shear field and the point spread function (PSF) vary across the images in a realistic manner. The variable fields enable a variety of metrics that are inaccessible to constant shear simulations, including a direct measure of the impact of shape measurement inaccuracies, and the impact of PSF size and ellipticity, on the shear power spectrum. To assess the impact of shape measurement bias for cosmic shear, we present a general pseudo-Cℓ formalism that propagates spatially varying systematics in cosmic shear through to power spectrum estimates. We also show how one-point estimators of bias can be extracted from variable shear simulations. The GREAT10 Galaxy Challenge received 95 submissions and saw a factor of 3 improvement in the accuracy achieved by other shape measurement methods. The best methods achieve sub-per cent average biases. We find a strong dependence on accuracy as a function of signal-to-noise ratio, and indications of a weak dependence on galaxy type and size. Some requirements for the most ambitious cosmic shear experiments are met above a signal-to-noise ratio of 20. These results have the caveat that the simulated PSF was a ground-based PSF. Our results are a snapshot of the accuracy of current shape measurement methods and are a benchmark upon which improvement can be brought. This provides a foundation for a better understanding of the strengths and limitations of shape measurement methods

Cosmic shear has been identified as the method with the most potential to constrain dark energy. To capitalize on this potential, it is necessary to measure galaxy shapes with great accuracy, which in turn requires a detailed model for the image blurring by the telescope and atmosphere, the point spread function (PSF). In general, the PSF varies with wavelength and therefore the PSF integrated over an observing filter depends on the spectrum of the object. For a typical galaxy the spectrum varies across the galaxy image, thus the PSF depends on the position within the image. We estimate the bias on the shear due to such colour gradients by modelling galaxies using two co-centred, co-elliptical Sérsic profiles, each with a different spectrum. We estimate the effect of ignoring colour gradients and find the shear bias from a single galaxy can be very large depending on the properties of the galaxy. We find that halving the filter width reduces the shear bias by a factor of about 5. We show that, to the first order, tomographic cosmic shear two point statistics depend on the mean shear bias over the galaxy population at a given redshift. For a single broad filter, and averaging over a small galaxy catalogue from Simard et al., we find a mean shear bias which is subdominant to the predicted statistical errors for future cosmic shear surveys. However, the true mean shear bias may exceed the statistical errors, depending on how accurately the catalogue represents the observed distribution of galaxies in the cosmic shear survey. We then investigate the bias on the shear for two-filter imaging and find that the bias is reduced by at least an order of magnitude. Lastly, we find that it is possible to calibrate galaxies for which colour gradients were ignored using two-filter imaging of a fair sample of noisy galaxies, if the galaxy model is known. For a signal-to-noise ratio of 25 the number of galaxies required in each tomographic redshift bin is of the order of 104

In the absence of any compelling physical model, cosmological systematics are often misrepresented as statistical effects and the approach of marginalizing 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 marginalizing 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)| ≲ 10−3 (1 +z)0.7 is required for a future all-sky photometric survey to yield unbiased cosmological parameter constraints to per cent accuracy. A module associated with the work in this paper is available through the open source icosmo code available at http://www.icosmo.org

Measurements of the power spectrum from large-scale structure surveys have to date assumed an equal-time approximation, where the full cross-correlation power spectrum of the matter density field evaluated at different times (or distances) has been approximated either by the power spectrum at a fixed time, or in an improved fashion, by a geometric mean $P(k; r_1, r_2)=[P(k; r_1) P(k; r_2)]^{1/2}$. In this paper we investigate the expected impact of the geometric mean ansatz, and present an application in assessing the impact on weak gravitational lensing cosmological parameter inference, using a perturbative unequal-time correlator. As one might expect, we find that the impact of this assumption is greatest at large separations in redshift $\Delta z > 0.3$ where the change in the amplitude of the matter power spectrum can be as much as $10$ percent for $k > 5h$Mpc$^{-1}$. However, of more concern is that the corrections for small separations, where the clustering is not close to zero, may not be negligibly small. In particular, we find that for a Euclid- or LSST-like weak lensing experiment the assumption of equal-time correlators may result in biased predictions of the cosmic shear power spectrum, and that the impact is strongly dependent on the amplitude of the intrinsic alignment signal. To compute unequal-time correlations to sufficient accuracy will require advances in either perturbation theory to high $k$-modes, or extensive use of simulations., Comment: 11 pages, 7 figures. Submitted to PRD

We present the Red-sequence Cluster Lensing Survey (RCSLenS), an application of the methods developed for the Canada France Hawaii Telescope Lensing Survey (CFHTLenS) to the ~785deg$^2$, multi-band imaging data of the Red-sequence Cluster Survey 2 (RCS2). This project represents the largest public, sub-arcsecond seeing, multi-band survey to date that is suited for weak gravitational lensing measurements. With a careful assessment of systematic errors in shape measurements and photometric redshifts we extend the use of this data set to allow cross-correlation analyses between weak lensing observables and other data sets. We describe the imaging data, the data reduction, masking, multi-colour photometry, photometric redshifts, shape measurements, tests for systematic errors, and a blinding scheme to allow for more objective measurements. In total we analyse 761 pointings with r-band coverage, which constitutes our lensing sample. Residual large-scale B-mode systematics prevent the use of this shear catalogue for cosmic shear science. The effective number density of lensing sources over an unmasked area of 571.7deg$^2$ and down to a magnitude limit of r~24.5 is 8.1 galaxies per arcmin$^2$ (weighted: 5.5 arcmin$^{-2}$) distributed over 14 patches on the sky. Photometric redshifts based on 4-band griz data are available for 513 pointings covering an unmasked area of 383.5 deg$^2$ We present weak lensing mass reconstructions of some example clusters as well as the full survey representing the largest areas that have been mapped in this way. All our data products are publicly available through CADC at http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/community/rcslens/query.html in a format very similar to the CFHTLenS data release., Comment: 21 pages, 16 figures, 4 tables, MNRAS in press, data release at http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/community/rcslens/query.html

With the advent of large-scale weak lensing surveys there is a need to understand how realistic, scale-dependent systematics bias cosmic shear and dark energy measurements, and how they can be removed. Here we describe how spatial variations in the amplitude and orientation of realistic image distortions convolve with the measured shear field, mixing the even-parity convergence and odd-parity modes, and bias the shear power spectrum. Many of these biases can be removed by calibration to external data, the survey itself, or by modelling in simulations. The uncertainty in the calibration must be marginalised over and we calculate how this propagates into parameter estimation, degrading the dark energy Figure-of-Merit. We find that noise-like biases affect dark energy measurements the most, while spikes in the bias power have the least impact, reflecting their correlation with the effect of cosmological parameters. We argue that in order to remove systematic biases in cosmic shear surveys and maintain statistical power effort should be put into improving the accuracy of the bias calibration rather than minimising the size of the bias. In general, this appears to be a weaker condition for bias removal. We also investigate how to minimise the size of the calibration set for a fixed reduction in the Figure-of-Merit. These results can be used to model the effect of biases and calibration on a cosmic shear survey accurately, assess their impact on the measurement of modified gravity and dark energy models, and to optimise surveys and calibration requirements., Comment: 10 pages, 3 figures

Measurements of the power spectrum from large-scale structure surveys have to date assumed an equal-time approximation, where the full cross-correlation power spectrum of the matter density field evaluated at different times (or distances) has been approximated either by the power spectrum at a fixed time, or in an improved fashion, by a geometric mean $P(k; r_1, r_2)=[P(k; r_1) P(k; r_2)]^{1/2}$. In this paper we investigate the expected impact of the geometric mean ansatz, and present an application in assessing the impact on weak gravitational lensing cosmological parameter inference, using a perturbative unequal-time correlator. As one might expect, we find that the impact of this assumption is greatest at large separations in redshift $\Delta z > 0.3$ where the change in the amplitude of the matter power spectrum can be as much as $10$ percent for $k > 5h$Mpc$^{-1}$. However, of more concern is that the corrections for small separations, where the clustering is not close to zero, may not be negligibly small. In particular, we find that for a Euclid- or LSST-like weak lensing experiment the assumption of equal-time correlators may result in biased predictions of the cosmic shear power spectrum, and that the impact is strongly dependent on the amplitude of the intrinsic alignment signal. To compute unequal-time correlations to sufficient accuracy will require advances in either perturbation theory to high $k$-modes, or extensive use of simulations., Comment: 11 pages, 7 figures. Submitted to PRD

With the advent of large-scale weak lensing surveys there is a need to understand how realistic, scale-dependent systematics bias cosmic shear and dark energy measurements, and how they can be removed. Here we describe how spatial variations in the amplitude and orientation of realistic image distortions convolve with the measured shear field, mixing the even-parity convergence and odd-parity modes, and bias the shear power spectrum. Many of these biases can be removed by calibration to external data, the survey itself, or by modelling in simulations. The uncertainty in the calibration must be marginalised over and we calculate how this propagates into parameter estimation, degrading the dark energy Figure-of-Merit. We find that noise-like biases affect dark energy measurements the most, while spikes in the bias power have the least impact, reflecting their correlation with the effect of cosmological parameters. We argue that in order to remove systematic biases in cosmic shear surveys and maintain statistical power effort should be put into improving the accuracy of the bias calibration rather than minimising the size of the bias. In general, this appears to be a weaker condition for bias removal. We also investigate how to minimise the size of the calibration set for a fixed reduction in the Figure-of-Merit. These results can be used to model the effect of biases and calibration on a cosmic shear survey accurately, assess their impact on the measurement of modified gravity and dark energy models, and to optimise surveys and calibration requirements., Comment: 10 pages, 3 figures

We present the Red-sequence Cluster Lensing Survey (RCSLenS), an application of the methods developed for the Canada France Hawaii Telescope Lensing Survey (CFHTLenS) to the ~785deg$^2$, multi-band imaging data of the Red-sequence Cluster Survey 2 (RCS2). This project represents the largest public, sub-arcsecond seeing, multi-band survey to date that is suited for weak gravitational lensing measurements. With a careful assessment of systematic errors in shape measurements and photometric redshifts we extend the use of this data set to allow cross-correlation analyses between weak lensing observables and other data sets. We describe the imaging data, the data reduction, masking, multi-colour photometry, photometric redshifts, shape measurements, tests for systematic errors, and a blinding scheme to allow for more objective measurements. In total we analyse 761 pointings with r-band coverage, which constitutes our lensing sample. Residual large-scale B-mode systematics prevent the use of this shear catalogue for cosmic shear science. The effective number density of lensing sources over an unmasked area of 571.7deg$^2$ and down to a magnitude limit of r~24.5 is 8.1 galaxies per arcmin$^2$ (weighted: 5.5 arcmin$^{-2}$) distributed over 14 patches on the sky. Photometric redshifts based on 4-band griz data are available for 513 pointings covering an unmasked area of 383.5 deg$^2$ We present weak lensing mass reconstructions of some example clusters as well as the full survey representing the largest areas that have been mapped in this way. All our data products are publicly available through CADC at http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/community/rcslens/query.html in a format very similar to the CFHTLenS data release., Comment: 21 pages, 16 figures, 4 tables, MNRAS in press, data release at http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/community/rcslens/query.html

In this paper we present results of applying the shear-ratio method to the RCSLenS data. The method takes the ratio of the mean of the weak lensing tangential shear signal about galaxy clusters, averaged over all clusters of the same redshift, in multiple background redshift bins. In taking a ratio the mass-dependency of the shear signal is cancelled-out leaving a statistic that is dependent on the geometric part of the lensing kernel only. We apply this method to 535 clusters and measure a cosmology-independent distance-redshift relation to redshifts z~1. In combination with Planck data the method lifts the degeneracies in the CMB measurements, resulting in cosmological parameter constraints of OmegaM=0.31 +/- 0.10 and w0 = -1.02 +/- 0.37, for a flat wCDM cosmology., Comment: 9 pages, 5 figures. Submitted to MNRAS

In this paper we investigate the impact that realistic scale-dependence systematic effects may have on cosmic shear tomography. We model spatially varying residual ellipticity and size variations in weak lensing measurements and propagate these through to predicted changes in the uncertainty and bias of cosmological parameters. We show that the survey strategy - whether it is regular or randomised - is an important factor in determining the impact of a systematic effect: a purely randomised survey strategy produces the smallest biases, at the expense of larger parameter uncertainties, and a very regularised survey strategy produces large biases, but unaffected uncertainties. However, by removing, or modelling, the affected scales (l-modes) in the regular cases the biases are reduced to negligible levels. We find that the integral of the systematic power spectrum is not a good metric for dark energy performance, and we advocate that systematic effects should be modelled accurately in real space, where they enter the measurement process, and their effect subsequently propagated into power spectrum contributions., Comment: 14 pages. Submitted to MNRAS

Here we present a Bayesian formalism for the goodness-of-fit that is the evidence for a fixed functional form over the evidence for all functions that are a general perturbation about this form. This is done under the assumption that the statistical properties of the data can be modelled by a multivariate Gaussian distribution. We use this to show how one can optimise an experiment to find evidence for a fixed function over perturbations about this function. We apply this formalism to an illustrative problem of measuring perturbations in the dark energy equation of state about a cosmological constant., Comment: Accepted to MNRAS. Full journal article available here http://mnras.oxfordjournals.org/content/452/2/1519.full

We study the correlations of the shear signal between triplets of sources in the Canada-France-Hawaii Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum. In contrast to previous studies, we adopted a non-Gaussian model of the data likelihood which is supported by our simulations of the survey. We find that for state-of-the-art surveys, similar to CFHTLenS, a Gaussian likelihood analysis is a reasonable approximation, albeit small differences in the parameter constraints are already visible. For future surveys we expect that a Gaussian model becomes inaccurate. Our algorithm for a refined non-Gaussian analysis and data compression is then of great utility especially because it is not much more elaborate if simulated data are available. Applying this algorithm to the third-order correlations of shear alone in a blind analysis, we find a good agreement with the standard cosmological model: $\Sigma_8$=$\sigma_8$ $(\Omega_{\rm m}/0.27)^{0.64}$=$0.79^{+0.08}_{-0.11}$ for a flat $\Lambda\rm CDM$ cosmology with $h=0.7\pm0.04$ ($68\%$ credible interval). Nevertheless our models provide only moderately good fits as indicated by $\chi^2/{\rm dof}=2.9$, including a $20\%$ r.m.s. uncertainty in the predicted signal amplitude. The models cannot explain a signal drop on scales around 15 arcmin, which may be caused by systematics. It is unclear whether the discrepancy can be fully explained by residual PSF systematics of which we find evidence at least on scales of a few arcmin. Therefore we need a better understanding of higher-order correlations of cosmic shear and their systematics to confidently apply them as cosmological probes., Comment: 21 pages, 13 figures, accepted by MNRAS; edit of arXiv abstract; files are unchanged

We investigate the capabilities of various stages of the SKA to perform world-leading weak gravitational lensing surveys. We outline a way forward to develop the tools needed for pursuing weak lensing in the radio band. We identify the key analysis challenges and the key pathfinder experiments that will allow us to address them in the run up to the SKA. We identify and summarize the unique and potentially very powerful aspects of radio weak lensing surveys, facilitated by the SKA, that can solve major challenges in the field of weak lensing. These include the use of polarization and rotational velocity information to control intrinsic alignments, and the new area of weak lensing using intensity mapping experiments. We show how the SKA lensing surveys will both complement and enhance corresponding efforts in the optical wavebands through cross-correlation techniques and by way of extending the reach of weak lensing to high redshift., Comment: 19 pages, 6 figures. Cosmology Chapter, Advancing Astrophysics with the SKA (AASKA14) Conference, Giardini Naxos (Italy), June 9th-13th 2014

In this paper we present results of applying the shear-ratio method to the RCSLenS data. The method takes the ratio of the mean of the weak lensing tangential shear signal about galaxy clusters, averaged over all clusters of the same redshift, in multiple background redshift bins. In taking a ratio the mass-dependency of the shear signal is cancelled-out leaving a statistic that is dependent on the geometric part of the lensing kernel only. We apply this method to 535 clusters and measure a cosmology-independent distance-redshift relation to redshifts z~1. In combination with Planck data the method lifts the degeneracies in the CMB measurements, resulting in cosmological parameter constraints of OmegaM=0.31 +/- 0.10 and w0 = -1.02 +/- 0.37, for a flat wCDM cosmology., Comment: 9 pages, 5 figures. Submitted to MNRAS