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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 $\sigma[m_0+15(m_1+m_3)+0.1(m_{-1}+m_5)]\leq 0.01$. 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

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)

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

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

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

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

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

We present weak lensing and X-ray analysis of 12 low mass clusters from the CFHTLenS and XMM-CFHTLS surveys. We combine these systems with high-mass systems from CCCP and low-mass systems from COSMOS 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., Comment: Analysis modified to include bias correction. Updated CCCP measurements. Comments are welcome, submitted to MNRAS, 26 pages, 20 figures

In this paper we present a power spectrum formalism that combines the full three-dimensional information from the galaxy ellipticity field, with information from the cosmic microwave background (CMB). We include in this approach galaxy cosmic shear and galaxy intrinsic alignments, CMB deflection, CMB temperature and CMB polarisation data; including the inter-datum power spectra between all quantities. We apply this to forecasting cosmological parameter errors for CMB and imaging surveys for Euclid-like, Planck, ACTPoL, and CoRE-like experiments. We show that the additional covariance between the CMB and ellipticity measurements can improve dark energy equation of state measurements by 15%, and the combination of cosmic shear and the CMB, from Euclid-like and CoRE-like experiments, could in principle measure the sum of neutrino masses with an error of 0.003 eV., Comment: Accepted to MNRAS

This paper presents the first application of 3D cosmic shear to a wide-field weak lensing survey. 3D cosmic shear is a technique that analyses weak lensing in three dimensions using a spherical harmonic approach, and does not bin data in the redshift direction. This is applied to CFHTLenS, a 154 square degree imaging survey with a median redshift of 0.7 and an effective number density of 11 galaxies per square arcminute usable for weak lensing. To account for survey masks we apply a 3D pseudo-Cl approach on weak lensing data, and to avoid uncertainties in the highly non-linear regime, we separately analyse radial wave numbers k<=1.5h/Mpc and k<=5.0h/Mpc, and angular wavenumbers l~400-5000. We show how one can recover 2D and tomographic power spectra from the full 3D cosmic shear power spectra and present a measurement of the 2D cosmic shear power spectrum, and measurements of a set of 2-bin and 6-bin cosmic shear tomographic power spectra; in doing so we find that using the 3D power in the calculation of such 2D and tomographic power spectra from data naturally accounts for a minimum scale in the matter power spectrum. We use 3D cosmic shear to constrain cosmologies with parameters OmegaM, OmegaB, sigma8, h, ns, w0, wa. For a non-evolving dark energy equation of state, and assuming a flat cosmology, lensing combined with WMAP7 results in h=0.78+/-0.12, OmegaM=0.252+/-0.079, sigma8=0.88+/-0.23 and w=-1.16+/-0.38 using only scales k<=1.5h/Mpc. We also present results of lensing combined with first year Planck results, where we find no tension with the results from this analysis, but we also find no significant improvement over the Planck results alone. We find evidence of a suppression of power compared to LCDM on small scales 1.5 < k < 5.0 h/Mpc in the lensing data, which is consistent with predictions of the effect of baryonic feedback on the matter power spectrum., Comment: Full journal article here http://mnras.oxfordjournals.org/content/442/2/1326.full.pdf+html

We outline the prospects for performing pioneering radio weak gravitational lensing analyses using observations from a potential forthcoming JVLA Sky Survey program. A large-scale survey with the JVLA can offer interesting and unique opportunities for performing weak lensing studies in the radio band, a field which has until now been the preserve of optical telescopes. In particular, the JVLA has the capacity for large, deep radio surveys with relatively high angular resolution, which are the key characteristics required for a successful weak lensing study. We highlight the potential advantages and unique aspects of performing weak lensing in the radio band. In particular, the inclusion of continuum polarisation information can greatly reduce noise in weak lensing reconstructions and can also remove the effects of intrinsic galaxy alignments, the key astrophysical systematic effect that limits weak lensing at all wavelengths. We identify a VLASS "deep fields" program (total area ~10-20 square degs), to be conducted at L-band and with high-resolution (A-array configuration), as the optimal survey strategy from the point of view of weak lensing science. Such a survey will build on the unique strengths of the JVLA and will remain unsurpassed in terms of its combination of resolution and sensitivity until the advent of the Square Kilometre Array. We identify the best fields on the JVLA-accessible sky from the point of view of overlapping with existing deep optical and near infra-red data which will provide crucial redshift information and facilitate a host of additional compelling multi-wavelength science., Comment: Submitted in response to NRAO's recent call for community white papers on the VLA Sky Survey (VLASS)

We present the first direct measurement of the galaxy-matter bispectrum as a function of galaxy luminosity, stellar mass, and SED type. Our analysis uses a galaxy-galaxy-galaxy lensing technique (G3L), on angular scales between 9 arcsec to 50 arcmin, to quantify (i) the excess surface mass density around galaxy pairs (excess mass hereafter) and (ii) the excess shear-shear correlations around single galaxies, both of which yield a measure of two types of galaxy-matter bispectra. We apply our method to the state-of-the-art Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), spanning 154 square degrees. This survey allows us to detect a significant change of the bispectra with lens properties. Measurements for lens populations with distinct redshift distributions become comparable by a newly devised normalisation technique. That will also aid future comparisons to other surveys or simulations. A significant dependence of the normalised G3L statistics on luminosity within -23

We present data products from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). CFHTLenS is based on the Wide component of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). It encompasses 154 deg^2 of deep, optical, high-quality, sub-arcsecond imaging data in the five optical filters u^*g'r'i'z'. The article presents our data processing of the complete CFHTLenS data set. We were able to obtain a data set with very good image quality and high-quality astrometric and photometric calibration. Our external astrometric accuracy is between 60-70 mas with respect to SDSS data and the internal alignment in all filters is around 30 mas. Our average photometric calibration shows a dispersion on the order of 0.01 to 0.03 mag for g'r'i'z' and about 0.04 mag for u^* with respect to SDSS sources down to i <= 21. In the spirit of the CFHTLS all our data products are released to the astronomical community via the Canadian Astronomy Data Centre. We give a description and how-to manuals of the public products which include image pixel data, source catalogues with photometric redshift estimates and all relevant quantities to perform weak lensing studies., Comment: 34 pages, 15 figures, 7 tables, submitted to MNRAS All CFHTLenS data products (image pixel data and lensing/photo-z catalogues) are publicly released to the community via CADC on the 1st of November 2012. Please vistit http://www.cfhtlens.org/ and http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/community/CFHTLens/query.html

A likelihood-based method for measuring weak gravitational lensing shear in deep galaxy surveys is described and applied to the Canada-France-Hawaii Telescope (CFHT) Lensing Survey (CFHTLenS). CFHTLenS comprises 154 sq deg of multicolour optical data from the CFHT Legacy Survey, with lensing measurements being made in the i' band to a depth i'(AB)<24.7, for galaxies with signal-to-noise ratio greater than about 10. The method is based on the lensfit algorithm described in earlier papers, but here we describe a full analysis pipeline that takes into account the properties of real surveys. The method creates pixel-based models of the varying point spread function (PSF) in individual image exposures. It fits PSF-convolved two-component (disk plus bulge) models, to measure the ellipticity of each galaxy, with bayesian marginalisation over model nuisance parameters of galaxy position, size, brightness and bulge fraction. The method allows optimal joint measurement of multiple, dithered image exposures, taking into account imaging distortion and the alignment of the multiple measurements. We discuss the effects of noise bias on the likelihood distribution of galaxy ellipticity. Two sets of image simulations that mirror the observed properties of CFHTLenS have been created, to establish the method's accuracy and to derive an empirical correction for the effects of noise bias., Comment: 24 pages, submitted to MNRAS. All CFHTLenS data products (image pixel data and lensing/photo-z catalogues) are publicly released to the community via CADC on the 1st of November 2012. Please visit the CFHTLenS site http://www.cfhtlens.org for further information

We present the results from the first public blind PSF reconstruction challenge, the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) Star Challenge. Reconstruction of a spatially varying PSF, sparsely sampled by stars, at non-star positions is a critical part in the image analysis for weak lensing where inaccuracies in the modelled ellipticity and size-squared can impact the ability to measure the shapes of galaxies. This is of importance because weak lensing is a particularly sensitive probe of dark energy, and can be used to map the mass distribution of large scale structure. Participants in the challenge were presented with 27,500 stars over 1300 images subdivided into 26 sets, where in each set a category change was made in the type or spatial variation of the PSF. Thirty submissions were made by 9 teams. The best methods reconstructed the PSF with an accuracy of ~0.00025 in ellipticity and ~0.00074 in size squared. For a fixed pixel scale narrower PSFs were found to be more difficult to model than larger PSFs, and the PSF reconstruction was severely degraded with the inclusion of an atmospheric turbulence model (although this result is likely to be a strong function of the amplitude of the turbulence power spectrum)., Comment: 23 pages, 7 figures; submitted to ApJS

In this paper we present results from the Mapping Dark Matter competition that expressed the weak lensing shape measurement task in its simplest form and as a result attracted over 700 submissions in 2 months and a factor of 3 improvement in shape measurement accuracy on high signal to noise galaxies, over previously published results, and a factor 10 improvement over methods tested on constant shear blind simulations. We also review weak lensing shape measurement challenges, including the Shear TEsting Programmes (STEP1 and STEP2) and the GRavitational lEnsing Accuracy Testing competitions (GREAT08 and GREAT10)., Comment: 20 pages, 12 figures. Solicited submission to New Astronomy Reviews

We describe a simple and fast method to correct ellipticity measurements of galaxies from the distortion by the instrumental and atmospheric point spread function (PSF), in view of weak lensing shear measurements. The method performs a classification of galaxies and associated PSFs according to measured shape parameters, and corrects the measured galaxy ellipticites by querying a large lookup table (LUT), built by supervised learning. We have applied this new method to the GREAT10 image analysis challenge, and present in this paper a refined solution that obtains the competitive quality factor of Q = 104, without any shear power spectrum denoising or training. Of particular interest is the efficiency of the method, with a processing time below 3 ms per galaxy on an ordinary CPU., Comment: 8 pages, 6 figures. Metric values updated according to the final GREAT10 analysis software (Kitching et al. 2012, MNRAS 423, 3163-3208), no qualitative changes. Associated code available at http://lastro.epfl.ch/megalut

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 shape measurement methods. The best methods achieve sub-percent average biases. We find a strong dependence in accuracy as a function of signal-to-noise, 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 continue. This provides a foundation for a better understanding of the strengths and limitations of shape measurement methods., Comment: Accepted to MNRAS

Here we present the results of various approaches to measure accurate colours and photometric redshifts (photo-z's) from wide-field imaging data. We use data from the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS) which have been re- processed by the CFHT Lensing Survey (CFHTLenS) team in order to carry out a number of weak gravitational lensing studies. An emphasis is put on the correction of systematic effects in the photo-z's arising from the different Point Spread Functions (PSF) in the five optical bands. Different ways of correcting these effects are discussed and the resulting photo-z accuracies are quantified by comparing the photo-z's to large spectroscopic redshift (spec-z) data sets. Careful homogenisation of the PSF between bands leads to increased overall accuracy of photo-z's. The gain is particularly pronounced at fainter magnitudes where galaxies are smaller and flux measurements are affected more by PSF-effects. We also study possible re- calibrations of the photometric zeropoints (ZPs) with the help of galaxies with known spec-z's. We find that if PSF-effects are properly taken into account, a re-calibration of the ZPs becomes much less important suggesting that previous such re-calibrations described in the literature could in fact be mostly corrections for PSF-effects rather than corrections for real inaccuracies in the ZPs. The implications of this finding for future surveys like KiDS, DES, LSST, or Euclid are mixed. On the one hand, ZP re-calibrations with spec-z's might not be as accurate as previously thought. On the other hand, careful PSF homogenisation might provide a way out and yield accurate, homogeneous photometry without the need for full spectroscopic coverage. This is the first paper in a series describing the technical aspects of CFHTLenS. (abridged), Comment: 15 pages, 10 figures, accepted by MNRAS, minor revisions

Cosmic shear has been identified as the method with the most potential to constrain dark energy. To capitalise on this potential it is necessary to measure galaxy shapes with great accuracy, which in turn requires a detailed model for the image blurring, 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-centered, co-elliptical Sersic 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 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, 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 S/N of 25 the number of galaxies required in each tomographic redshift bin is of order 1e4., Comment: 13 pages of main text, 10 figures

Here we present an investigation into using nested sampling algorithms in cosmological likelihood analysis. We present a new nested sampling algorithm, ESNested, that uses Evolution Strategies for sample proposals. This quickly finds the maximum for complex likelihoods and provides an accurate measure of the Bayesian evidence, with no prior assumptions about the shape of the likelihood surface. We present the first cosmological constraints using Evolution Strategies, from WMAP 7, HST and SNIa data using likelihood and data provided with CosmoMC. We find a significantly higher maximum likelihood than that found with other methods. We compare the performance of ESNested with the publicly available MultiNest and CosmoNest algorithms, in i) finding the maximum likelihood ii) calculating confidence contours in projected parameter spaces and iii) calculating the Bayesian evidence. We find that none of the algorithms provide a single solution for all of these products in general. Our recommendation is that multiple sampling methods should be used in cosmological likelihood analysis and that algorithms should be tailored to perform optimally for each of these requirements. These results have a resonance with the well-known No Free Lunch theorem., Comment: This paper has been withdrawn by the authors. Accepted to MNRAS. However further sophistications, add-ons, and changes to the algorithms suggest that these initial introductory results could be improved; as a precaution we have fully withdrawn this article

We present a new method that deals with the uncertainty in matter-clustering in cosmic shear power spectrum analysis that arises mainly due to poorly understood nonlinear baryonic processes on small-scales. We show that the majority of information about dark energy physics contained in the shear power comes from these small-scales; removing these nonlinear scales from a cosmic shear analysis results in a 50% cut in the accuracy of measurements of dark energy parameters, marginalizing over all other parameters. In this paper we propose a method to recover the information on small-scales by allowing cosmic shear surveys to measure the nonlinear matter power spectrum themselves and marginalize over all possible power spectra using path integrals. Information is still recoverable in these nonlinear regimes from the geometric part of weak lensing. In this self-calibration regime we find we recover 90% of the information on dark energy. Including an informative prior, we find the nonlinear matter power spectrum needs to be accurately known to 1% down to k=50 h/Mpc to recover 99% of the dark energy information. This presents a significant theoretical challenge to understand baryonic effects on the scale of galaxy haloes. However self-calibration from weak lensing may also provide observational input to help constrain baryon physics., Comment: 6 pages, 5 figures, submitted to MNRAS

Here we present a number of improvements to weak lensing 3D power spectrum analysis, 3D cosmic shear, that uses the shape and redshift information of every galaxy to constrain cosmological parameters. We show how photometric redshift probability distributions for individual galaxies can be directly included in this statistic with no averaging. We also include the Limber approximation, considerably simplifying full 3D cosmic shear analysis, and we investigate its range of applicability. Finally we show the relationship between weak lensing tomography and the 3D cosmic shear field itself; the steps connecting them being the Limber approximation, a harmonic-space transform and a discretisation in wavenumber. Each method has its advantages: 3D cosmic shear analysis allows straightforward inclusion of all relevant modes, thus ensuring minimum error bars, and direct control of the range of physical wavenumbers probed, to avoid the uncertain highly nonlinear regime. On the other hand, tomography is more convenient for checking systematics through direct investigation of the redshift dependence of the signal. Finally, for tomography, we suggest that the angular modes probed should be redshift-dependent, to recover some of the 3D advantages., Comment: Accepted to MNRAS. 15 pages, 7 figures

We present a path-integral likelihood formalism that extends parameterized likelihood analyses to include continuous functions. The method finds the maximum likelihood point in function-space, and marginalizes over all possible functions, under the assumption of a Gaussian-distributed function-space. We apply our method to the problem of removing unknown systematic functions in two topical problems for dark energy research : scale-dependent galaxy bias in redshift surveys; and galaxy intrinsic alignments in cosmic shear surveys. We find that scale-dependent galaxy bias will degrade information on cosmological parameters unless the fractional variance in the bias function is known to 10%. Measuring and removing intrinsic alignments from cosmic shear surveys with a flat-prior can reduce the dark energy Figure-of-Merit by 20%, however provided that the scale and redshift-dependence is known to better than 10% with a Gaussian-prior, the dark energy Figure-of-Merit can be enhanced by a factor of two with no extra assumptions., Comment: 11 pages, 4 figures, submitted to MNRAS

We present general, analytic methods for Cosmological likelihood analysis and solve the "many-parameters" problem in Cosmology. Maxima are found by Newton's Method, while marginalization over nuisance parameters, and parameter errors and covariances are estimated by analytic marginalization of an arbitrary likelihood function with flat or Gaussian priors. We show that information about remaining parameters is preserved by marginalization. Marginalizing over all parameters, we find an analytic expression for the Bayesian evidence for model selection. We apply these methods to data described by Gaussian likelihoods with parameters in the mean and covariance. This method can speed up conventional likelihood analysis by orders of magnitude when combined with Monte-Carlo Markov Chain methods, while Bayesian model selection becomes effectively instantaneous., Comment: 12 pages, 4 figures, submitted to MNRAS

The energy density of the Universe is dominated by dark energy and dark matter, two mysterious components which pose some of the most important questions in fundamental science today. Euclid is a high-precision survey mission designed to answer these questions by mapping the geometry of the dark Universe. Euclid's Visible-NIR imaging and spectroscopy of the entire extragalactic sky will further produce extensive legacy science for various fields of astronomy. Over the 2008-2009 period, Euclid has been the object of an ESA Assessment Phase in which the study of the Euclid Imaging instrument was under the responsibility of the Euclid Imaging Consortium (EIC). The EIC Science Book presents the studies done by the EIC science working groups in the context of this study phase. We first give a brief description of the Euclid mission and of the imaging instrument and surveys. We then summarise the primary and legacy science which will be achieved with the Euclid imaging surveys, along with the simulations and data handling scheme which have been developed to optimise the instrument and ensure its science performance., Comment: 214 Latex pages, including full list of authors on page 3. Full resolution document available at http://www.euclid-imaging.net

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 tophat basis set requires an even higher order. We show that the common approach used for finding the marginalised 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 ., Comment: 10 pages, 7 figures

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 MNRAS

We extend the Bayesian model fitting shape measurement method presented in Miller et al. (2007) and use the method to estimate the shear from the Shear TEsting Programme simulations (STEP). The method uses a fast model fitting algorithm which uses realistic galaxy profiles and analytically marginalises over the position and amplitude of the model by doing the model fitting in Fourier space. This is used to find the full posterior probability in ellipticity so that the shear can be estimated in a fully Bayesian way. The Bayesian shear estimation allows measurement bias arising from the presence of random noise to be removed. In this paper we introduce an iterative algorithm that can be used to estimate the intrinsic ellipticity prior and show that this is accurate and stable. By using the method to estimate the shear from the STEP1 simulations we find the method to have a shear bias of m ~ 0.005 and a variation in shear offset with PSF type of sigma_c ~ 0.0002. These values are smaller than for any method presented in the STEP1 publication that behaves linearly with shear. Using the method to estimate the shear from the STEP2 simulations we find than the shear bias and offset are m ~ 0.002 and c ~ -0.0007 respectively. In addition we find that the bias and offset are stable to changes in magnitude and size of the galaxies. Such biases should yield any cosmological constraints from future weak lensing surveys robust to systematic effects in shape measurement., Comment: 19 pages, 11 Figures, 2 Tables, submitted to MNRAS. Companion paper to Miller et al. (2007) arXiv:0708.2340

In this paper we investigate the potential of 3D cosmic shear to constrain massive neutrino parameters. We find that if the total mass is substantial (near the upper limits from LSS, but setting aside the Ly alpha limit for now), then 3D cosmic shear + Planck is very sensitive to neutrino mass and one may expect that a next generation photometric redshift survey could constrain the number of neutrinos N_nu and the sum of their masses m_nu to an accuracy of dN_nu ~ 0.08 and dm_nu ~ 0.03 eV respectively. If in fact the masses are close to zero, then the errors weaken to dN_nu ~ 0.10 and dm_nu~0.07 eV. In either case there is a factor 4 improvement over Planck alone. We use a Bayesian evidence method to predict joint expected evidence for N_nu and m_nu. We find that 3D cosmic shear combined with a Planck prior could provide `substantial' evidence for massive neutrinos and be able to distinguish `decisively' between many competing massive neutrino models. This technique should `decisively' distinguish between models in which there are no massive neutrinos and models in which there are massive neutrinos with |N_nu-3| > 0.35 and m_nu > 0.25 eV. We introduce the notion of marginalised and conditional evidence when considering evidence for individual parameter values within a multi-parameter model., Comment: 9 pages, 2 Figures, 2 Tables, submitted to Physical Review D

We present an investigation into the potential effect of systematics inherent in multi-band wide field surveys on the dark energy equation of state determination for two 3D weak lensing methods. The weak lensing methods are a geometric shear-ratio method and 3D cosmic shear. The analysis here uses an extension of the Fisher matrix framework to jointly include photometric redshift systematics, shear distortion systematics and intrinsic alignments. We present results for DUNE and Pan-STARRS surveys. We show that assuming systematic parameters are fixed, but possibly biased, results in potentially large biases in dark energy parameters. We quantify any potential bias by defining a Bias Figure of Merit. We also show the effect on the dark energy Figure of Merit of marginalising over each systematic parameter individually. We find that the largest effect on the Figure of Merit comes from uncertainty in the photometric redshift systematic parameters. These can reduce the Figure of Merit by up to a factor of 2 to 4 in both 3D weak lensing methods, if no informative prior on the systematic parameters is applied. Shear distortion systematics have a smaller overall effect. Intrinsic alignment effects can reduce the Figure of Merit by up to a further factor of 2. This, however, is a worst case scenario. By including prior information on systematic parameters the Figure of Merit can be recovered to a large extent. We conclude that, as a rule of thumb, given a realistic current understanding of intrinsic alignments and photometric redshifts, then including all three primary systematic effects reduces the Figure of Merit by at most a factor of 2, but that in reality this factor should be much less. [abridged], Comment: 20 pages, 11 figures, submitted to MNRAS