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We present forecasts from the combination of the <jats:italic>Euclid<\/jats:italic> weak lensing and photometric galaxy clustering data on the parameters describing four interesting and representative non-minimal dark matter models: a mixture of cold and warm dark matter relics; unstable dark matter decaying either into massless or massive relics; and dark matter undergoing feeble interactions with relativistic relics. We modelled these scenarios at the level of the non-linear matter power spectrum using emulators trained on dedicated <jats:italic>N<\/jats:italic>-body simulations. We used a mock <jats:italic>Euclid<\/jats:italic> likelihood and Monte Carlo Markov chains to fit mock data and infer error bars on dark matter parameters marginalised over other parameters. We find that the <jats:italic>Euclid<\/jats:italic> photometric probe (alone or in combination with cosmic microwave background data from the <jats:italic>Planck<\/jats:italic> satellite) will be sensitive to the effect of each of the four dark matter models considered here. The improvement will be particularly spectacular for decaying and interacting dark matter models. With <jats:italic>Euclid<\/jats:italic>, the bounds on some dark matter parameters can improve by up to two orders of magnitude compared to current limits. We discuss the dependence of predicted uncertainties on different assumptions: the inclusion of photometric galaxy clustering data, the minimum angular scale taken into account, and modelling of baryonic feedback effects. We conclude that the <jats:italic>Euclid<\/jats:italic> mission will be able to measure quantities related to the dark sector of particle physics with unprecedented sensitivity. This will provide important information for model building in high-energy physics. Any hint of a deviation from the minimal cold dark matter paradigm would have profound implications for cosmology and particle physics.<\/jats:p>","DOI":"10.1051\/0004-6361\/202451611","type":"journal-article","created":{"date-parts":[[2024,12,5]],"date-time":"2024-12-05T19:44:20Z","timestamp":1733427860000},"page":"A249","source":"Crossref","is-referenced-by-count":4,"title":["<i>Euclid<\/i> preparation"],"prefix":"10.1051","volume":"693","author":[{"name":"Euclid Collaboration","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7627-353X","authenticated-orcid":false,"given":"J.","family":"Lesgourgues","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0001-9987-1433","authenticated-orcid":false,"given":"J.","family":"Schwagereit","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1662-1042","authenticated-orcid":false,"given":"J.","family":"Bucko","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2539-2472","authenticated-orcid":false,"given":"G.","family":"Parimbelli","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2560-536X","authenticated-orcid":false,"given":"S. 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