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We study the morphology of convergence maps by perturbatively reconstructing their Minkowski functionals (MFs). We present a systematic study using a set of three generalized skew spectra as a function of source redshift and smoothing angular scale. These spectra denote the leading-order corrections to the Gaussian MFs in the quasi-linear regime. They can also be used as independent statistics to probe the bispectrum. Using an approach based on pseudo- S ℓs, we show how these spectra will allow the 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 ℓ 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 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. [ABSTRACT FROM AUTHOR]

A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l 1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous 'dark core' – an overdense region with no optical counterpart – which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at |$99{{\ \rm per\ cent}}$| confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data. [ABSTRACT FROM AUTHOR]

We introduce the skew-spectrum statistic for weak lensing convergence κ 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 κ 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. [ABSTRACT FROM AUTHOR]

Recent studies have demonstrated that secondary non-Gaussianity induced by gravity will be detected with a high signal-to-noise ratio (S/N) by future and even by on-going weak lensing surveys. One way to characterize 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. squeezed, equilateral, isosceles and 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. [ABSTRACT FROM AUTHOR]

Until recently, mass-mapping techniques for weak gravitational lensing convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstruction uncertainties, without making strong assumptions of Gaussianity. In previous work, we presented a sparse hierarchical Bayesian formalism for convergence reconstruction that addresses this shortcoming. Here, we draw on the concept of local credible intervals (cf. Bayesian error bars) as an extension of the uncertainty quantification techniques previously detailed. These uncertainty quantification techniques are benchmarked against those recovered via Px-MALA – a state-of-the-art proximal Markov chain Monte Carlo (MCMC) algorithm. We find that, typically, our recovered uncertainties are everywhere conservative (never underestimate the uncertainty, yet the approximation error is bounded above), of similar magnitude and highly correlated with those recovered via Px-MALA. Moreover, we demonstrate an increase in computational efficiency of |$\mathcal {O}(10^6)$| when using our sparse Bayesian approach over MCMC techniques. This computational saving is critical for the application of Bayesian uncertainty quantification to large-scale stage IV surveys such as LSST and Euclid. [ABSTRACT FROM AUTHOR]

Context. 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 (SFRs) is contested, with observations of galaxy mergers showing reduced, enhanced, and highly enhanced star formation. Aims. We aim to determine the effect of galaxy mergers on the SFR of galaxies using statistically large samples of galaxies, totalling over 200 000, which is over a large redshift range from 0.0 to 4.0. Methods. We trained and used convolutional neural networks to create binary merger identifications (merger or non-merger) in the SDSS, KiDS, and CANDELS imaging surveys. We then compared the SFR, with the galaxy main sequence subtracted, of the merging and non-merging galaxies to determine what effect, if any, a galaxy merger has on SFR. Results. 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 is above the galaxy main sequence, the higher the fraction is for galaxy mergers. Conclusions. 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. [ABSTRACT FROM AUTHOR]

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 show how spatially varying image distortions are convolved with the shear field, mixing convergence E and B modes, and bias the observed shear power spectrum. In practise, many of these biases can be removed by calibration to data or simulations. The uncertainty in this calibration is marginalized over, and we calculate how this propagates into parameter estimation and degrades 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. 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 minimizing the size of the bias. In general, this appears to be a weaker condition for bias removal. We also investigate how to minimize the size of the calibration set for a fixed reduction in the Figure-of-Merit. Our results can be used to correctly model the effect of biases and calibration on a cosmic shear survey, assess their impact on the measurement of modified gravity and dark energy models, and to optimize survey and calibration requirements. [ABSTRACT FROM AUTHOR]

We present the Red Cluster Sequence Lensing Survey (RCSLenS), an application of the methods developed for the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS) to the ∼785 deg2, multi-band imaging data of the Red-sequence Cluster Survey 2. 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 571.7 deg2 and down to a magnitude limit of r ∼ 24.5 is 8.1 galaxies per arcmin2 (weighted: 5.5 arcmin−2) distributed over 14 patches on the sky. Photometric redshifts based on four-band griz data are available for 513 pointings covering an unmasked area of 383.5 deg2. 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 Canadian Astronomy Data Centre 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. [ABSTRACT FROM AUTHOR]

The covariance of the matter power spectrum is a key element of the analysis of galaxy clustering data. Independent realizations of observational measurements can be used to sample the covariance, nevertheless statistical sampling errors will propagate into the cosmological parameter inference potentially limiting the capabilities of the upcoming generation of galaxy surveys. The impact of these errors as function of the number of realizations has been previously evaluated for Gaussian distributed data. However, non-linearities in the late-time clustering of matter cause departures from Gaussian statistics. Here, we address the impact of non-Gaussian errors on the sample covariance and precision matrix errors using a large ensemble of N-body simulations. In the range of modes where finite volume effects are negligible (0.1 ≲ k [h Mpc-1] ≲ 1.2), we find deviations of the variance of the sample covariance with respect to Gaussian predictions above ~10 per cent at k > 0.3 h Mpc-1. Over the entire range these reduce to about ~5 per cent for the precision matrix. Finally, we perform a Fisher analysis to estimate the effect of covariance errors on the cosmological parameter constraints. In particular, assuming Euclid-like survey characteristics we find that a number of independent realizations larger than 5000 is necessary to reduce the contribution of sampling errors to the cosmological parameter uncertainties at subpercent level. We also show that restricting the analysis to large scales k ≲ 0.2 h Mpc-1 results in a considerable loss in constraining power, while using the linear covariance to include smaller scales leads to an underestimation of the errors on the cosmological parameters. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the impact that realistic scale-dependent systematic effects may have on cosmic shear tomography. We model spatially varying residual galaxy ellipticity and galaxy 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 randomized -- is an important factor in determining the impact of a systematic effect: a purely randomized survey strategy produces the smallest biases, at the expense of larger parameter uncertainties, and a very regularized 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. [ABSTRACT FROM AUTHOR]

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 optimize 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. [ABSTRACT FROM AUTHOR]

In this paper, we present a power spectrum formalism that combines the full 3D 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 polarization data; including the interdatum power spectra between all quantities. We apply this to forecasting cosmological parameter errors for CMB and imaging surveys and show that the additional covariance between the CMB and ellipticity measurements can improve dark energy equation of state measurements by 30 per cent. We present predictions for Euclid-like, Planck, ACTPoL, and CoRE-like experiments and show that 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, and the dark energy equation of state with an error on w0 of less than 0.02. [ABSTRACT FROM AUTHOR]

We study the correlations of the shear signal between triplets of sources in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum. In contrast to previous studies, we adopt 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: Σ8=σ8(Ωm/0.27)0.64=0.79+0.08-0.11 for a flat Λ cold dark matter cosmology with h = 0.7 ± 0.04 (68-percent credible interval). Nevertheless our models provide only moderately good fits as indicated by χ2/dof = 2.9, including a 20-percent rms 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 point spread function 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. [ABSTRACT FROM AUTHOR]

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 wavenumbers k ≤ 1.5 and 5.0 h Mpc−1, 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 ΩM, ΩB, σ8, h , ns, w0 and wa. For a non-evolving dark energy equation of state, and assuming a flat cosmology, lensing combined with Wilkinson Microwave Anisotropy Probe 7 results in h = 0.78 ± 0.12, ΩM = 0.252 ± 0.079, σ8 = 0.88 ± 0.23 and w = −1.16 ± 0.38 using only scales k ≤ 1.5 h Mpc−1. 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 Lambda cold dark matter (LCDM) on small scales 1.5 < k ≤ 5.0 h Mpc−1 in the lensing data, which is consistent with predictions of the effect of baryonic feedback on the matter power spectrum. [ABSTRACT FROM AUTHOR]

We investigate the extent to which cosmic size magnification may be used to complement cosmic shear in weak gravitational lensing surveys, with a view to obtaining high-precision estimates of cosmological parameters. Using simulated galaxy images, we find that unbiased estimation of the convergence field is possible using galaxies with angular sizes larger than the point spread function (PSF) and signal-to-noise ratio in excess of 10. The statistical power is similar to, but not quite as good as, cosmic shear, and it is subject to different systematic effects. Application to ground-based data will be challenging, with relatively large empirical corrections required to account for the fact that many galaxies are smaller than the PSF, but for space-based data with 0.1-0.2 arcsec resolution, the size distribution of galaxies brighter than i ≃ 24 is almost ideal for accurate estimation of cosmic size magnification. [ABSTRACT FROM AUTHOR]

We present the first direct measurement of the galaxy–matter bispectrum as a function of galaxy luminosity, stellar mass and type of spectral energy distribution (SED). Our analysis uses a galaxy–galaxy–galaxy lensing technique (G3L), on angular scales between 9 arcsec and 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 normalization technique. That will also aid future comparisons to other surveys or simulations. A significant dependence of the normalized G3L statistics on luminosity within −23 ≤ Mr ≤ −18 and stellar mass within 5 × 109 M⊙ ≤ M* ≤ 2 × 1011 M⊙ is found (h = 0.73). Both bispectra exhibit a stronger signal for more luminous lenses or those with higher stellar mass (up to a factor of 2–3). This is accompanied by a steeper equilateral bispectrum for more luminous or higher stellar mass lenses for the excess mass. Importantly, we find the excess mass to be very sensitive to galaxy type as recently predicted with semi-analytic galaxy models: luminous (Mr < −21) late-type galaxies show no detectable signal, while all excess mass detected for luminous galaxies seems to be associated with early-type galaxies. We also present the first observational constraints on third-order stochastic galaxy biasing parameters. [ABSTRACT FROM AUTHOR]

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 deg2 of multi-colour 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 νSN ≳ 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 (disc plus bulge) models to measure the ellipticity of each galaxy, with Bayesian marginalization 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. [ABSTRACT FROM AUTHOR]

ABSTRACT 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. [ABSTRACT FROM AUTHOR]

ABSTRACT Here we present the results of various approaches to measure accurate colours and photometric redshifts (photo- z) from wide-field imaging data. We use data from the Canada-France-Hawaii Telescope Legacy Survey which have been re-processed by the Canada-France-Hawaii Telescope 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 arising from the different point spread functions (PSFs) 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 to large spectroscopic redshift (spec- z) data sets. Careful homogenization of the PSF between bands leads to increased overall accuracy of photo- z. The gain is particularly pronounced at fainter magnitudes where galaxies are smaller and flux measurements are affected more by PSF effects. We discuss ways of defining more secure subsamples of galaxies as well as a shape- and colour-based star-galaxy separation method, and we present redshift distributions for different magnitude limits. We also study possible re-calibrations of the photometric zero-points (ZPs) with the help of galaxies with known spec- z. 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 the Kilo Degree Survey (KiDS), Dark Energy Survey (DES), Large Synoptic Survey Telescope or Euclid are mixed. On the one hand, ZP re-calibrations with spec- z values might not be as accurate as previously thought. On the other hand, careful PSF homogenization 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. [ABSTRACT FROM AUTHOR]

ABSTRACT 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. [ABSTRACT FROM AUTHOR]

ABSTRACT 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 non-linear baryonic processes on small scales. We show that the majority of information about new physics contained in the shear power comes from these small scales. Removing these non-linear scales from a cosmic shear analysis results in 50 per cent 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 non-linear matter power spectrum themselves and marginalize over all possible power spectra using path integrals. Information is still recoverable in these non-linear regimes from the geometric part of weak lensing. In this self-calibration regime we recover 90 per cent of the information on dark energy. Including an informative prior, we find that the non-linear matter power spectrum needs to be accurately known to 1 per cent down to k= 50 h−1 Mpc, or a scale of 120 kpc, to recover 99 per cent of the dark energy information. This presents a significant theoretical challenge to understand baryonic effects on the scale of galaxy haloes. [ABSTRACT FROM AUTHOR]

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 discretization 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 non-linear 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

ABSTRACT We present a path integral likelihood formalism that extends parametrized 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 per cent. Measuring and removing intrinsic alignments from cosmic shear surveys with a flat prior can reduce the dark energy figure of merit by 20 per cent, however provided that the scale and redshift dependence is known to better than 10 per cent with a Gaussian prior, the dark energy figure of merit can be enhanced by a factor of 2 with no extra assumptions. [ABSTRACT FROM AUTHOR]

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, expanding the log-likelihood to second order, 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. These methods can speed up conventional likelihood analysis by orders of magnitude when combined with Markov chain Monte Carlo methods, while Bayesian model selection becomes effectively instantaneous. [ABSTRACT FROM AUTHOR]

Weak gravitational lensing provides a sensitive probe of cosmology by measuring the mass distribution and the geometry of the low-redshift Universe. We show how an all-sky weak lensing tomographic survey can jointly constrain different sets of cosmological parameters describing dark energy, massive neutrinos (hot dark matter) and the primordial power spectrum. In order to put all sectors on an equal footing, we introduce a new parameter β, the second-order running spectral index. Using the Fisher matrix formalism with and without cosmic microwave background (CMB) priors, we examine how the constraints vary as the parameter set is enlarged. We find that weak lensing with CMB priors provides robust constraints on dark energy parameters and can simultaneously provide strong constraints on all three sectors. We find that the dark energy sector is largely insensitive to the inclusion of the other cosmological sectors. Implications for the planning of future surveys are discussed. [ABSTRACT FROM AUTHOR]

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 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 sourceicosmo code available at . [ABSTRACT FROM AUTHOR]

Within the context of constraining an expansion of the dark energy equation of state 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 , 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 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 . It also allows for the reconstruction of the redshift sensitivity of the experiment to changes in . However, the technique is sensitive to both the order and the basis set choice. Publicly available code is available as part oficosmo at . [ABSTRACT FROM AUTHOR]

In this paper, we extend the Bayesian model fitting shape measurement method presented in Miller et al., and use the method to estimate the shear from the Shear TEsting Programme simulations (STEP). The method uses a fast model fitting algorithm that uses realistic galaxy profiles and analytically marginalizes 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. The shear is then estimated in a Bayesian way from this posterior probability surface. The Bayesian 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. We present results using the STEP parametrization that relates the input shear to the estimated shear by introducing a bias m and an offset c: . The average number density of galaxies used in the STEP1 analysis was 9 per square arcminute, for STEP2 the number density was 30 per square arcminute. By using the method to estimate the shear from the STEP1 simulations we find the method to have a shear bias of and a variation in shear offset with point spread function type of . Using the method to estimate the shear from the STEP2 simulations we find that the shear bias and offset are and , respectively. In addition, we find that the bias and offset are stable to changes in the 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. Finally, we present an alternative to the STEP parametrization by using a quality factor that relates the intrinsic shear variance in a simulation to the variance in shear that is measured and show that the method presented has an average of which is at least a factor of 10 times better than other shape measurement methods. [ABSTRACT FROM AUTHOR]

We present an investigation into the potential effect of systematics inherent in multiband 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 include jointly photometric redshift systematics, shear distortion systematics and intrinsic alignments. Using analytic parametrizations of these three primary systematic effects allows an isolation of systematic parameters of particular importance. 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. By marginalizing over extra systematic parameters, such biases are negated at the expense of an increase in the cosmological parameter errors. We show the effect on the dark energy Figure of Merit of marginalizing over each systematic parameter individually. We also show the overall reduction in the Figure of Merit due to all three types of systematic effects. Based on some assumption of the likely level of systematic errors, 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, within the assumptions of the parametrizations used. By including prior information on systematic parameters, the Figure of Merit can be recovered to a large extent, and combined constraints from 3D cosmic shear and shear ratio are robust to systematics. 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. [ABSTRACT FROM AUTHOR]

The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing measurement with maximal signal-to-noise ratio, coupled with estimation of measurement errors. The distinction between likelihood-based and Bayesian methods is discussed. Systematic biases in the Bayesian method may be evaluated as part of the fitting process, and overall such an approach should yield unbiased shear estimation without requiring external calibration from simulations. The principal disadvantage of model fitting for large surveys is the computational time required, but here an algorithm is presented that enables large surveys to be analysed in feasible computation times. The method and algorithm is tested on simulated galaxies from the Shear TEsting Programme (STEP). [ABSTRACT FROM AUTHOR]

The Fisher matrix approach allows one to calculate in advance how well a given experiment will be able to estimate model parameters, and has been an invaluable tool in experimental design. In the same spirit, we present here a method to predict how well a given experiment can distinguish between different models, regardless of their parameters. From a Bayesian viewpoint, this involves computation of the Bayesian evidence. In this paper, we generalize the Fisher matrix approach from the context of parameter fitting to that of model testing, and show how the expected evidence can be computed under the same simplifying assumption of a Gaussian likelihood as the Fisher matrix approach for parameter estimation. With this ‘Laplace approximation’ all that is needed to compute the expected evidence is the Fisher matrix itself. We illustrate the method with a study of how well upcoming and planned experiments should perform at distinguishing between dark energy models and modified gravity theories. In particular, we consider the combination of 3D weak lensing, for which planned and proposed wide-field multiband imaging surveys will provide suitable data, and probes of the expansion history of the Universe, such as proposed supernova and baryonic acoustic oscillations surveys. We find that proposed large-scale weak-lensing surveys from space should be able readily to distinguish General Relativity from modified gravity models. [ABSTRACT FROM AUTHOR]

We present the first application of the 3D cosmic shear method developed in Heavens, Kitching & Taylor and the geometric shear-ratio analysis developed in Taylor et al., to the COMBO-17 data set. 3D cosmic shear has been used to analyse galaxies with redshift estimates from two random COMBO-17 fields covering 0.52 deg2 in total, providing a conditional constraint in the (σ8, Ωm) plane as well as a conditional constraint on the equation of state of dark energy, parametrized by a constant . The plane analysis constrained the relation between σ8 and Ωm to be , in agreement with a 2D cosmic shear analysis of COMBO-17. The 3D cosmic shear conditional constraint on w using the two random fields is . The geometric shear-ratio analysis has been applied to the A901/2 field, which contains three small galaxy clusters. Combining the analysis from the A901/2 field, using the geometric shear-ratio analysis, and the two random fields, using 3D cosmic shear, w is conditionally constrained to . The errors presented in this paper are shown to agree with Fisher matrix predictions made in Heavens, Kitching & Taylor and Taylor et al. When these methods are applied to large data sets, as expected soon from surveys such as Pan-STARRS and VST-KIDS, the dark energy equation of state could be constrained to an unprecedented degree of accuracy. [ABSTRACT FROM AUTHOR]

We adapt the Jain–Taylor (2003) shear-ratio geometric lensing method to measure the dark energy equation of state, and its time derivative from dark matter haloes in cosmologies with arbitrary spatial curvature. The full shear-ratio covariance matrix is calculated for lensed sources, including the intervening large-scale structure and photometric redshift errors as additional sources of noise, and a maximum likelihood method for applying the test is presented. Decomposing the lensing matter distribution into dark matter haloes we calculate the parameter covariance matrix for an arbitrary experiment. Combining with the expected results from the cosmic microwave background (CMB) we design an optimal survey for probing dark energy. This shows that a targeted survey imaging 60 of the largest clusters in a hemisphere with five-band optical photometric redshifts to a median galaxy depth of could measure to a marginal 1σ error of . We marginalize over all other parameters including w a, where the equation of state is parametrized in terms of scalefactor a as . For higher accuracy a large-scale photometric redshift survey is required, where the largest gain in signal arises from the numerous ≈1014 M⊙ haloes corresponding to medium-sized galaxy clusters. Combined with the expected Planck Surveyor results, such a near-future five-band survey covering 10 000 deg2 to could measure w0 to and . A stronger combined constraint is put on w measured at the pivot redshift of . We compare and combine the geometric test with the cosmological and dark energy parameters measured from planned baryon acoustic oscillation (BAO) and supernova Type Ia experiments, and find that the geometric test results combine with a significant reduction in errors due to different degeneracies. A combination of geometric lensing, CMB and BAO experiments could achieve and with a pivot redshift constraint of at . Simple relations are presented that show how our lensing results can be scaled to other telescope classes and survey parameters. [ABSTRACT FROM AUTHOR]

We present parameter estimation forecasts for present and future 3D cosmic shear surveys. We demonstrate in particular that, in conjunction with results from cosmic microwave background (CMB) experiments, the properties of dark energy can be estimated with very high precision with large-scale, fully 3D weak-lensing surveys. In particular, a five-band, 10 000-deg2 ground-based survey of galaxies to a median redshift of could achieve 1σ marginal statistical errors, in combination with the constraints expected from the CMB Planck Surveyor, of and . We parametrize the redshift evolution of w by where a is the scalefactor. Such a survey is achievable with a wide-field camera on a 4-m class telescope. The error on the value of w at an intermediate pivot redshift of is constrained to . We compare and combine the 3D weak-lensing constraints with the cosmological and dark energy parameters measured from planned baryon acoustic oscillation (BAO) and supernova Type Ia experiments, and find that 3D weak lensing significantly improves the marginalized errors on w0 and w a in combination, and provides constraints on w( z) at a unique redshift through the lensing effect. A combination of 3D weak-lensing, CMB and BAO experiments could achieve and . We also show how our results can be scaled to other telescopes and survey designs. Fully 3D weak shear analysis avoids the loss of information inherent in tomographic binning, and we also show that the sensitivity to systematic errors in photometric redshift is much less. In conjunction with the fact that the physics of lensing is very soundly based, the analysis here demonstrates that deep, wide-angle 3D weak-lensing surveys are extremely promising for measuring dark energy properties. [ABSTRACT FROM AUTHOR]

ABSTRACT Here we present the results of various approaches to measure accurate colours and photometric redshifts (photo- z) from wide-field imaging data. We use data from the Canada-France-Hawaii Telescope Legacy Survey which have been re-processed by the Canada-France-Hawaii Telescope 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 arising from the different point spread functions (PSFs) 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 to large spectroscopic redshift (spec- z) data sets. Careful homogenization of the PSF between bands leads to increased overall accuracy of photo- z. The gain is particularly pronounced at fainter magnitudes where galaxies are smaller and flux measurements are affected more by PSF effects. We discuss ways of defining more secure subsamples of galaxies as well as a shape- and colour-based star-galaxy separation method, and we present redshift distributions for different magnitude limits. We also study possible re-calibrations of the photometric zero-points (ZPs) with the help of galaxies with known spec- z. 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 the Kilo Degree Survey (KiDS), Dark Energy Survey (DES), Large Synoptic Survey Telescope or Euclid are mixed. On the one hand, ZP re-calibrations with spec- z values might not be as accurate as previously thought. On the other hand, careful PSF homogenization 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. [ABSTRACT FROM AUTHOR]

In this article, we review model selection predictions for modified gravity scenarios as an explanation for the observed acceleration of the expansion history of the Universe. We present analytical procedures for calculating expected Bayesian evidence values in two cases: (i) that modified gravity is a simple parametrized extension of general relativity (GR; two nested models), such that a Bayes' factor can be calculated, and (ii) that we have a class of non-nested models where a rank-ordering of evidence values is required. We show that, in the case of a minimal modified gravity parametrization, we can expect large area photometric and spectroscopic surveys, using three-dimensional cosmic shear and baryonic acoustic oscillations, to 'decisively' distinguish modified gravity models over GR (or vice versa), with odds of ≫1:100. It is apparent that the potential discovery space for modified gravity models is large, even in a simple extension to gravity models, where Newton's constant G is allowed to vary as a function of time and length scale. On the time and length scales where dark energy dominates, it is only through large-scale cosmological experiments that we can hope to understand the nature of gravity.