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The GRavitational lEnsing Accuracy Testing 2008 (GREAT08) Challenge focuses on a problem that is of crucial importance for future observations in cosmology. The shapes of distant galaxies can be used to determine the properties of dark energy and the nature of gravity, because light from those galaxies is bent by gravity from the intervening dark matter. The observed galaxy images appear distorted, although only slightly, and their shapes must be precisely disentangled from the effects of pixelisation, convolution and noise. The worldwide gravitational lensing community has made significant progress in techniques to measure these distortions via the Shear TEsting Program (STEP). Via STEP, we have run challenges within our own community, and come to recognise that this particular image analysis problem is ideally matched to experts in statistical inference, inverse problems and computational learning. Thus, in order to continue the progress seen in recent years, we are seeking an infusion of new ideas from these communities. This document details the GREAT08 Challenge for potential participants. Please visit www.great08challenge.info for the latest information.

GRavitational lEnsing Accuracy Testing 2010 (GREAT10) is a public image analysis challenge aimed at the development of algorithms to analyze astronomical images. Specifically, the challenge is to measure varying image distortions in the presence of a variable convolution kernel, pixelization and noise. This is the second in a series of challenges set to the astronomy, computer science and statistics communities, providing a structured environment in which methods can be improved and tested in preparation for planned astronomical surveys. GREAT10 extends upon previous work by introducing variable fields into the challenge. The \"Galaxy Challenge\" involves the precise measurement of galaxy shape distortions, quantified locally by two parameters called shear, in the presence of a known convolution kernel. Crucially, the convolution kernel and the simulated gravitational lensing shape distortion both now vary as a function of position within the images, as is the case for real data. In addition, we introduce the \"Star Challenge\" that concerns the reconstruction of a variable convolution kernel, similar to that in a typical astronomical observation. This document details the GREAT10 Challenge for potential participants. Continually updated information is also available from www.greatchallenges.info.

We present a pedagogical review of the halo model, a flexible framework that can describe the distribution of matter and its tracers on non-linear scales for both conventional and exotic cosmological models. We start with the premise that the complex structure of the cosmic web can be described by the sum of its individual components: dark matter, gas, and galaxies, all distributed within spherical haloes with a range of masses. The halo properties are specified through a series of simulation-calibrated ingredients including the halo mass function, non-linear halo bias and a dark matter density profile that can additionally account for the impact of baryon feedback. By incorporating a model of the galaxy halo occupation distribution, the properties of central and satellite galaxies, their non-linear bias and intrinsic alignment can be predicted. Through analytical calculations of spherical collapse in exotic cosmologies, the halo model also provides predictions for non-linear clustering in beyond-\\(\\Lambda\\)CDM models. The halo model has been widely used to model observations of a variety of large-scale structure probes, most notably as the primary technique to model the underlying non-linear matter power spectrum. By documenting these varied and often distinct use cases, we seek to further coherent halo model analyses of future multi-tracer observables. This review is accompanied by the release of pyhalomodel: https://github.com/alexander-mead/pyhalomodel , flexible software to conduct a wide range of halo-model calculations.

We present an independent cosmic shear analysis of the non-cosmological B-mode distortions within the public first year data from the Dark Energy Survey (DES). We find no significant detection of B-modes in a full tomographic analysis of the primary METACALIBRATION shear catalogue. This is in contrast to the secondary IM3SHAPE shear catalogue, where we detect B- modes at a significance of \\(\\sim 3\\sigma\\) with a pattern that is consistent with the B-mode signature of a repeating additive shear bias across the survey. We use the COSEBIs statistic to cleanly separate the B-modes from the gravitational lensing signal (E-modes). We find good agreement between the measured E-modes and their theoretical expectation given the DES cosmological parameter constraints.

We present an updated version of the HMcode augmented halo model that can be used to make accurate predictions of the non-linear matter power spectrum over a wide range of cosmologies. Major improvements include modelling of BAO damping in the power spectrum and an updated treatment of massive neutrinos. We fit our model to simulated power spectra and show that we can match the results with an RMS error of 2.5 per cent across a range of cosmologies, scales \\(k < 10\\,h\\mathrm{Mpc}^{-1}\\), and redshifts \\(z<2\\). The error rarely exceeds 5 per cent and never exceeds 16 per cent. The worst-case errors occur at \\(z\\simeq2\\), or for cosmologies with unusual dark-energy equations of state. This represents a significant improvement over previous versions of HMcode, and over other popular fitting functions, particularly for massive-neutrino cosmologies with high neutrino mass. We also present a simple halo model that can be used to model the impact of baryonic feedback on the power spectrum. This six-parameter physical model includes gas expulsion by AGN feedback and encapsulates star formation. By comparing this model to data from hydrodynamical simulations we demonstrate that the power spectrum response to feedback is matched at the \\(<1\\) per cent level for \\(z<1\\) and \\(k<20\\,h\\mathrm{Mpc}^{-1}\\). We also present a single-parameter variant of this model, parametrized in terms of feedback strength, which is only slightly less accurate. We make code available for our non-linear and baryon models at https://github.com/alexander-mead/HMcode and it is also available within CAMB and soon within CLASS.

We present a method to refine photometric redshift galaxy catalogs by comparing their color-space matching with overlapping spectroscopic calibration data. We focus on cases where photometric redshifts (photo-\\(z\\)) are estimated empirically. Identifying galaxies that are poorly represented in spectroscopic data is crucial, as their photo-\\(z\\) may be unreliable due to extrapolation beyond the training sample. Our approach uses a self-organizing map (SOM) to project a multi-dimensional parameter space of magnitudes and colors onto a 2-D manifold, allowing us to analyze the resulting patterns as a function of various galaxy properties. Using SOM, we compare the Kilo-Degree Survey bright galaxy sample (KiDS-Bright), limited to \\(r<20\\) mag, with various spectroscopic samples, including the Galaxy And Mass Assembly (GAMA). Our analysis reveals that GAMA under-represents KiDS-Bright at its faintest (\\(r\\gtrsim19.5\\)) and highest-redshift (\\(z\\gtrsim0.4\\)) ranges, however no strong trends in color or stellar mass. By incorporating additional spectroscopic data from the SDSS, 2dF, and early DESI, we identify SOM cells where photo-\\(z\\) are estimated suboptimally. We derive a set of SOM-based criteria to refine the photometric sample and improve photo-\\(z\\) statistics. For the KiDS-Bright sample, this improvement is modest: exclusion of the least represented 20% of the sample reduces photo-\\(z\\) scatter by less than 10%. We conclude that GAMA, used for KiDS-Bright photo-\\(z\\) training, is sufficiently representative for reliable redshift estimation across most of the color space. Future spectroscopic data from surveys such as DESI should be better suited for exploiting the full improvement potential of our method.

We present an analytical description of the probability distribution function (PDF) of the smoothed three-dimensional matter density field for modified gravity and dark energy. Our approach, based on the principles of Large Deviations Theory, is applicable to general extensions of the standard \\(\\Lambda\\)CDM cosmology. We show that late-time changes to the law of gravity and background expansion can be included through Einstein-de Sitter spherical collapse dynamics combined with linear theory calculations and a calibration measurement of the non-linear variance of the smoothed density field from a simple numerical simulation. In a comparison to \\(N\\)-body simulations for \\(f(R)\\), DGP and evolving dark energy theories, we find percent level accuracy around the peak of the distribution for predictions in the mildly non-linear regime. A Fisher forecast of an idealised experiment with a Euclid-like survey volume demonstrates the power of combining measurements of the 3D matter PDF with the 3D matter power spectrum. This combination is shown to halve the uncertainty on parameters for an evolving dark energy model, relative to a power spectrum analysis on its own. The PDF is also found to substantially increase the detection significance for small departures from General Relativity, with improvements of up to six times compared to the power spectrum alone. This analysis is therefore very promising for future studies including non-Gaussian statistics, as it has the potential to alleviate the reliance of these analyses on expensive high resolution simulations and emulators.

We present constraints on the flat \\(\\Lambda\\)CDM cosmological model through a joint analysis of galaxy abundance, galaxy clustering and galaxy-galaxy lensing observables with the Kilo-Degree Survey. Our theoretical model combines a flexible conditional stellar mass function, to describe the galaxy-halo connection, with a cosmological N-body simulation-calibrated halo model to describe the non-linear matter field. Our magnitude-limited bright galaxy sample combines 9-band optical-to-near-infrared photometry with an extensive and complete spectroscopic training sample to provide accurate redshift and stellar mass estimates. Our faint galaxy sample provides a background of accurately calibrated lensing measurements. We constrain the structure growth parameter \\(S_8=\\sigma_8\\sqrt{\\Omega_{\\mathrm{m}}/0.3}=0.773^{+0.028}_{-0.030}\\), and the matter density parameter \\(\\Omega_{\\mathrm{m}}=0.290^{+0.021}_{-0.017}\\). The galaxy-halo connection model adopted in the work is shown to be in agreement with previous studies. Our constraints on cosmological parameters are comparable to, and consistent with, joint \\(3\\times2{\\mathrm{pt}}\\) clustering-lensing analyses that additionally include a cosmic shear observable. This analysis therefore brings attention to the significant constraining power in the often-excluded non-linear scales for galaxy clustering and galaxy-galaxy lensing observables. By adopting a theoretical model that accounts for non-linear halo bias, halo exclusion, scale-dependent galaxy bias and the impact of baryon feedback, this work demonstrates the potential and a way forward to include non-linear scales in cosmological analyses. Varying the width of the satellite galaxy distribution with an additional parameter yields a strong preference for sub-Poissonian variance, improving the goodness of fit by 0.18 in reduced \\(\\chi^{2}\\) value compared to a fixed Poisson distribution.

We determine the error introduced in a joint halo model analysis of galaxy-galaxy lensing and galaxy clustering observables when adopting the standard approximation of linear halo bias. Considering the Kilo-Degree Survey, we forecast that ignoring the non-linear halo bias would result in up to 5\\(\\sigma\\) offsets in the recovered cosmological parameters describing structure growth, \\(S_8\\), and the matter density parameter, \\(\\Omega_{\\mathrm{m}}\\). We include the scales \\(10^{-1.3}

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