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Unfortunately, much of the cosmological information is encoded on 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 <jats:italic>Euclid<\/jats:italic> cosmic shear and <jats:italic>Planck<\/jats:italic> 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 non-linear corrections lead to biased parameter estimates, especially when the analysis is extended into the highly non-linear regime, with the Hubble constant, <jats:italic>H<\/jats:italic><jats:sub>0<\/jats:sub>, and the clustering amplitude, <jats:italic>\u03c3<\/jats:italic><jats:sub>8<\/jats:sub>, affected the most. Improvements in the modelling of non-linear scales will therefore be needed if we are to resolve the current tension with more and better data. For a given prescription for the non-linear power spectrum, using different corrections for baryon physics does not significantly impact the precision of <jats:italic>Euclid<\/jats:italic>, 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 <jats:italic>Euclid<\/jats:italic> cosmic shear data, it is therefore essential to improve the accuracy of the recipes that account for non-linear structure formation, as well as the modelling of the impact of astrophysical processes that redistribute the baryons.<\/jats:p>","DOI":"10.1051\/0004-6361\/202039835","type":"journal-article","created":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T07:58:38Z","timestamp":1619164718000},"page":"A100","source":"Crossref","is-referenced-by-count":40,"title":["<i>Euclid<\/i>: Impact of non-linear and baryonic feedback prescriptions on cosmological parameter estimation from weak lensing cosmic shear"],"prefix":"10.1051","volume":"649","author":[{"given":"M.","family":"Martinelli","sequence":"first","affiliation":[]},{"given":"I.","family":"Tutusaus","sequence":"additional","affiliation":[]},{"given":"M.","family":"Archidiacono","sequence":"additional","affiliation":[]},{"given":"S.","family":"Camera","sequence":"additional","affiliation":[]},{"given":"V. 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