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We computed the values of these higher order effects using analytic expressions and calculated the impact on cosmological parameter estimations using the Fisher matrix formalism. We reviewed 24 effects and determined the ones that potentially need to be accounted for, namely: the reduced shear approximation, magnification bias, source-lens clustering, source obscuration, local Universe effects, and the flat Universe assumption. After computing these effects explicitly and calculating their cosmological parameter biases, using a maximum multipole of<jats:italic>\u2113<\/jats:italic>\u2004=\u20045000, we find that the magnification bias, source-lens clustering, source obscuration, and local Universe terms individually produce significant (&gt; 0.25<jats:italic>\u03c3<\/jats:italic>) cosmological biases in one or more parameters; accordingly, these effects must be accounted for and warrant further investigation. In total, we find biases in \u03a9<jats:sub>m<\/jats:sub>, \u03a9<jats:sub>b<\/jats:sub>,<jats:italic>h<\/jats:italic>, and<jats:italic>\u03c3<\/jats:italic><jats:sub>8<\/jats:sub>of 0.73<jats:italic>\u03c3<\/jats:italic>, 0.28<jats:italic>\u03c3<\/jats:italic>, 0.25<jats:italic>\u03c3<\/jats:italic>, and \u22120.79<jats:italic>\u03c3<\/jats:italic>, respectively, for the flat \u039bCDM. For the<jats:italic>w<\/jats:italic><jats:sub>0<\/jats:sub><jats:italic>w<\/jats:italic><jats:sub><jats:italic>a<\/jats:italic><\/jats:sub>CDM case, we found biases in \u03a9<jats:sub>m<\/jats:sub>, \u03a9<jats:sub>b<\/jats:sub>,<jats:italic>h<\/jats:italic>,<jats:italic>n<\/jats:italic><jats:sub>s<\/jats:sub>,<jats:italic>\u03c3<\/jats:italic><jats:sub>8<\/jats:sub>, and<jats:italic>w<\/jats:italic><jats:sub><jats:italic>a<\/jats:italic><\/jats:sub>of 1.49<jats:italic>\u03c3<\/jats:italic>, 0.35<jats:italic>\u03c3<\/jats:italic>, \u22121.36<jats:italic>\u03c3<\/jats:italic>, 1.31<jats:italic>\u03c3<\/jats:italic>, \u22120.84<jats:italic>\u03c3<\/jats:italic>, and \u22120.35<jats:italic>\u03c3<\/jats:italic>, respectively. These are increased relative to the \u039bCDM due to additional degeneracies as a function of redshift and scale.<\/jats:p>","DOI":"10.1051\/0004-6361\/202346110","type":"journal-article","created":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T19:48:31Z","timestamp":1706298511000},"page":"A138","source":"Crossref","is-referenced-by-count":12,"title":["<i>Euclid<\/i>preparation"],"prefix":"10.1051","volume":"684","author":[{"name":"Euclid Collaboration","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3721-4232","authenticated-orcid":false,"given":"A. 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