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Aims. The Euclid space telescope will measure the shapes and redshifts of galaxies to reconstruct the expansion history of the Universe and the growth of cosmic structures. The estimation of the expected performance of the experiment, in terms of predicted constraints on cosmological parameters, has so far relied on various individual methodologies and numerical implementations, which were developed for different observational probes and for the combination thereof. In this paper we present validated forecasts, which combine both theoretical and observational ingredients for different cosmological probes. This work is presented to provide the community with reliable numerical codes and methods for Euclid cosmological forecasts.Methods. We describe in detail the methods adopted for Fisher matrix forecasts, which were applied to galaxy clustering, weak lensing, and the combination thereof. We estimated the required accuracy for Euclid forecasts and outline a methodology for their development. We then compare and improve different numerical implementations, reaching uncertainties on the errors of cosmological parameters that are less than the required precision in all cases. Furthermore, we provide details on the validated implementations, some of which are made publicly available, in different programming languages, together with a reference training-set of input and output matrices for a set of specific models. These can be used by the reader to validate their own implementations if required.Results. We present new cosmological forecasts for Euclid. We find that results depend on the specific cosmological model and remaining freedom in each setting, for example flat or non-flat spatial cosmologies, or different cuts at non-linear scales. The numerical implementations are now reliable for these settings. We present the results for an optimistic and a pessimistic choice for these types of settings. We demonstrate that the impact of cross-correlations is particularly relevant for models beyond a cosmological constant and may allow us to increase the dark energy figure of merit by at least a factor of three. ; Academy of Finland European Commission Agenzia Spaziale Italiana (ASI) Belgian Federal Science Policy Office Canadian Euclid Consortium Centre National D'etudes Spatiales Deutsches Zentrum fur Luft-and Raumfahrt Danish Space Research Institute Fundacao para a Cienca e a Tecnologia Spanish Government National Aeronautics & Space Administration (NASA) 80NM0018D0004 Netherlandse Onderzoekschool Voor Astronomie Norvegian Space Center Romanian Space Agency State Secretariat for Education, Research and Innovation (SERI) at the Swiss Space O ffice (SSO) United Kingdom Space Agency Ministry of Education, Universities and Research (MIUR) Ministry of Education, Universities and Research (MIUR) L. 232/2016 European Research Council through the Darklight Advanced Research Grant 291521 Ministry of Education, Universities and Research (MIUR) Centre National D'etudes Spatiales Fonds de la Recherche Scientifique - FNRS Swiss National Science Foundation (SNSF) European Commission NASA ROSES grant 12-EUCLID12-0004 UK Science & Technology Facilities Council ST/N000668/1 ST/S000437/1 UK Space Agency ST/N00180X/1 D-ITP consortium, a program of the NWO - the OCW Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) CONICYT FONDECYT 1200171 Spanish Ministry of Science, Innovation and Universities ESP2017-89838-C3-1-R H2020 programme of the European Commission 776247 German Research Foundation (DFG) Transregio 33 International Max Planck Research School for Astronomy and Astrophysics at the University of Bonn International Max Planck Research School for Astronomy and Astrophysics at the University of Cologne Bonn-Cologne Graduate School for Physics and Astronomy Royal Society of London European Research Council (ERC) 617656

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-zs 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 designed a challenge using emulated Euclid data drawn from three photometric surveys of the COSMOS field. The data was divided into two samples: one calibration sample for which photometry and redshifts were 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 the sources they consider unfit for use in cosmological analyses. The performance of each method was 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, that is to say 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. We find that no machine-learning method provides good results in the regions of galaxy color-space that are sparsely populated by spectroscopic-redshifts, for example z> 1. However they generally perform better than template-fitting methods at low redshift (z< 0.7), indicating that template-fitting methods do not use all of the information contained in the photometry. We introduce metrics that quantify both photo-z precision and completeness of the samples (post-rejection), since both contribute to the final figure of merit of the science goals of the survey (e.g., cosmic shear from Euclid). Template-fitting methods provide the best results in these metrics, but we show that a combination of template-fitting results and machine-learning results with rejection criteria can outperform any individual method. On this basis, we argue that further work in identifying how to best select between machine-learning and template-fitting approaches for each individual galaxy should be pursued as a priority. ; Sinergia program of the Swiss National Science Foundation German Research Foundation (DFG) Ts 17/2-1 Istituto Nazionale Astrofisica (INAF) Agenzia Spaziale Italiana (ASI) 2018-23-HH.0 1.05.01.88.04 European Space Agency European Commission Agenzia Spaziale Italiana (ASI) Belgian Federal Science Policy Office Canadian Euclid Consortium Centre National D'etudes Spatiales Danish Space Research Institute Portuguese Foundation for Science and Technology European Commission Spanish Government National Aeronautics & Space Administration (NASA) Netherlandse Onderzoekschool Voor Astronomie Norwegian Space Agency Romanian Space Agency State Secretariat for Education, Research and Innovation (SERI) at the Swiss Space O ffice (SSO) United Kingdom Space Agency

Planck Collaboration. ; The characterization of the Galactic foregrounds has been shown to be the main obstacle in thechallenging quest to detect primordial B-modes in the polarized microwave sky. We make use of the Planck-HFI 2015 data release at high frequencies to place new constraints on the properties of the polarized thermal dust emission at high Galactic latitudes. Here, we specifically study the spatial variability of the dust polarized spectral energy distribution (SED), and its potential impact on the determination of the tensor-to-scalar ratio, r. We use the correlation ratio of the angular power spectra between the 217 and 353 GHz channels as a tracer of these potential variations, computed on different high Galactic latitude regions, ranging from 80% to 20% of the sky. The new insight from Planck data is a departure of the correlation ratio from unity that cannot be attributed to a spurious decorrelation due to the cosmic microwave background, instrumental noise, or instrumental systematics. The effect is marginally detected on each region, but the statistical combination of all the regions gives more than 99% confidence for this variation in polarized dust properties. In addition, we show that the decorrelation increases when there is a decrease in the mean column density of the region of the sky being considered, and we propose a simple power-law empirical model for this dependence, which matches what is seen in the Planck data. We explore the effect that this measured decorrelation has on simulations of the BICEP2-Keck Array/Planck analysis and show that the 2015 constraints from these data still allow a decorrelation between the dust at 150 and 353 GHz that is compatible with our measured value. Finally, using simplified models, we show that either spatial variation of the dust SED or of the dust polarization angle are able to produce decorrelations between 217 and 353 GHz data similar to the values we observe in the data. ; The Planck Collaboration acknowledges the support of: ESA; CNES, and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, J.A., and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement No. 267934. ; Peer Reviewed