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With the immense number of images, data, and sources that Euclid will deliver, the consortium will be in a unique position to create/provide/construct legacy catalogues. The latter will have exquisite imaging quality and good near-infrared spectroscopy, with impact on many areas of galaxy science. These proceedings review the prospects and scientific output that Euclid will be able to achieve in areas of galaxy and active galactic nucleus (AGN) evolution, the local and primeval Universe, studies of the Milky Way and stellar populations, supernovae (SN) and transients, Solar System objects, exoplanets, strong lensing and galaxy clusters., Comment: 6 pages, contribution to the ICHEP2022 conference proceedings accompanying the ''Euclid in a nutshell'' and ''Euclid: performance on main cosmological parameter science'' contributions

Euclid will observe 15 000 deg$^2$ of the darkest sky, in regions free of contamination by light from our Galaxy and our Solar System. Three "Euclid Deep Fields" surveys covering around 40 deg$^2$ in total will extend the scientific scope of the mission to the high-redshift Universe. The complete survey will be constituted by hundreds of thousands of images and several tens of petabytes of data. About 10 billion sources will be observed. With these images Euclid will probe the expansion history of the Universe and the evolution of cosmic structures. This will be achieved by measuring the effect on galaxy shapes due to dark matter gravitational lensing, and by reconstructing the three-dimensional distribution of cosmic structures from the measured spectroscopic redshifts of galaxies and clusters of galaxies. These proceedings present the implications for cosmology and cosmological constraints of this unprecedented data set. Of particular interest are the expected constraints on the nature of dark energy., Comment: 6 pages, contribution to the ICHEP 2022 conference proceedings, accompanying the "Euclid in a nutshell" and "Euclid legacy science prospects" contributions

Euclid is a European Space Agency (ESA) mission designed to constrain the properties of dark energy and gravity via weak gravitational lensing and galaxy clustering. It will carry out a wide area imaging and spectroscopy survey in visible and near-infrared bands, covering approximately 15 000 deg2 of the extragalactic sky in six years. Euclid will be equipped with a 1.2 m diameter Silicon Carbide (SiC) mirror telescope feeding two instruments built by the Euclid Consortium: a high-quality panoramic visible imager and a near-infrared photometer and spectrograph. These proceedings briefly describe the satellite and its instruments, which are optimised for pristine point spread function and reduced stray light, producing very crisp images. Furthermore, we summarise the survey strategy, the global scheduling, and the preparations for the satellite commissioning and the Science Data Centers to produce scientific data., Comment: 6 pages, 3 figures, contribution to the ICHEP 2022 conference proceedings, accompanying the "Euclid: performance on main cosmological parameter science" and "Euclid legacy science prospects" contributions

We propose a computationally feasible estimator for the needlet trispectrum, which develops earlier work on the bispectrum by Donzelli et al. (2012). Our proposal seems to enjoy a number of useful properties, in particular a) the construction exploits the localization properties of the needlet system, and hence it automatically handles masked regions; b) the procedure incorporates a quadratic correction term to correct for the presence of instrumental noise and sky-cuts; c) it is possible to provide analytic results on its statistical properties, which can serve as a guidance for simulations. The needlet trispectrum we present here provides the natural building blocks for the efficient estimation of nonlinearity parameters on CMB data, and in particular for the third order constants $g_{NL}$ and $\tau_{NL}$., Comment: 3 pages, 1 figure, proceedings of IAU 306 Symposium Statistical Challenges in 21st Century Cosmology