The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg² of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

We investigate the astrophysics of radio-emitting star-forming galaxies and active galactic nuclei (AGNs) and elucidate their statistical properties in the radio band, including luminosity functions, redshift distributions, and number counts at sub-mJy flux levels, which will be crucially probed by next-generation radio continuum surveys. Specifically, we exploit the model-independent approach by Mancuso et al. to compute the star formation rate functions, the AGN duty cycles, and the conditional probability of a star-forming galaxy to host an AGN with given bolometric luminosity. Coupling these ingredients with the radio emission properties associated with star formation and nuclear activity, we compute relevant statistics at different radio frequencies and disentangle the relative contribution of star-forming galaxies and AGNs in different radio luminosity, radio flux, and redshift ranges. Finally, we highlight that radio-emitting star-forming galaxies and AGNs are expected to host supermassive black holes accreting with different Eddington ratio distributions and to occupy different loci in the galaxy main-sequence diagrams. These specific predictions are consistent with current data sets but need to be tested with larger statistics via future radio data with multiband coverage on wide areas, as will become routinely achievable with the advent of the Square Kilometre Array and its precursors.

We aim to provide a holistic view on the typical size and kinematic evolution of massive early-type galaxies (ETGs) that encompasses their high-z star-forming progenitors, their high-z quiescent counterparts, and their configurations in the local Universe. Our investigation covers the main processes playing a relevant role in the cosmic evolution of ETGs. Specifically, their early fast evolution comprises biased collapse of the low angular momentum gaseous baryons located in the inner regions of the host dark matter halo; cooling, fragmentation, and infall of the gas down to the radius set by the centrifugal barrier; further rapid compaction via clump/gas migration toward the galaxy center, where strong heavily dust-enshrouded star formation takes place and most of the stellar mass is accumulated; and ejection of substantial gas amount from the inner regions by feedback processes, which causes a dramatic puffing-up of the stellar component. In the late slow evolution, passive aging of stellar populations and mass additions by dry merger events occur. We describe these processes relying on prescriptions inspired by basic physical arguments and by numerical simulations to derive new analytical estimates of the relevant sizes, timescales, and kinematic properties for individual galaxies along their evolution. Then we obtain quantitative results as a function of galaxy mass and redshift, and compare them to recent observational constraints on half-light size R _e , on the ratio v/σ between rotation velocity and velocity dispersion (for gas and stars) and on the specific angular momentum j _⋆ of the stellar component; we find good consistency with the available multiband data in average values and dispersion, both for local ETGs and for their z ∼ 1–2 star-forming and quiescent progenitors. The outcomes of our analysis can provide hints to gauge sub-grid recipes implemented in simulations, to tune numerical experiments focused on specific processes, and to plan future multiband, high-resolution observations on high-redshift star-forming and quiescent galaxies with next-generation facilities.

We investigate the merging rates of compact binaries in galaxies and the related detection rate of gravitational wave (GW) events with AdvLIGO/Virgo and with the Einstein Telescope. To this purpose, we rely on three basic ingredients: (i) the redshift-dependent galaxy statistics provided by the latest determination of the star formation rate functions from UV+far-IR/(sub)millimeter/radio data; (ii) star formation and chemical enrichment histories for individual galaxies, modeled on the basis of observations; and (iii) compact remnant mass distribution and prescriptions for merging of compact binaries from stellar evolution simulations. We present results for the intrinsic birth rate of compact remnants, the merging rates of compact binaries, GW detection rates, and GW counts, attempting to differentiate the outcomes among black hole–black hole, neutron star–neutron star, and black hole–neutron star mergers and to estimate their occurrence in disk and spheroidal host galaxies. We compare our approach with the one based on cosmic star formation rate density and cosmic metallicity, exploited by many literature studies; the merging rates from the two approaches are in agreement within the overall astrophysical uncertainties. We also investigate the effects of galaxy-scale strong gravitational lensing of GW in enhancing the rate of detectable events toward high redshift. Finally, we discuss the contribution of undetected GW emission from compact binary mergers to the stochastic background.