ESA Voyage 2050 white paper: Unveiling the faint ultraviolet Universe

New and unique science opportunities in several different fields of astrophysics are offered by conducting spectroscopic studies of the Universe in the ultraviolet (UV), a wavelength regime that is not accessible from the ground. We present some of the scientific challenges that can be addressed with a space-based mission in 2035 - 2050. (1) By detecting the intergalactic medium in emission it will be possible to unveil the cosmic web, whose existence is predicted by current theories of structure formation, but it has not been probed yet. (2) Observations of the neutral gas distribution (by mapping the Lyman-alpha emission) in low-redshift galaxy cluster members will clarify the efficiency with which ram-pressure stripping removes the gas from galaxies and the role of the environment in quenching star formation. (3) By observing statistical samples of supernovae in the UV it will be possible to characterize the progenitor population of core-collapse supernovae, providing the initial conditions for any forward-modeling simulation and allowing the community to progress in the understanding of the explosion mechanism of stars and the final stages of stellar evolution. (4) Targeting populations of accreting white dwarfs in globular clusters it will be possible to constrain the evolution and fate of these stars and investigate the properties of the most compact systems with the shortest orbital periods which are expected to be the brightest low frequency gravitational wave sources. A UV-optimized telescope (wavelength range ~ 90 - 350 nm), equipped with a panoramic integral field spectrograph with a large field of view (FoV ~ 1 x 1 arcmin^2), with medium spectral (R = 4000) and spatial (~ 1" - 3") resolution will allow the community to simultaneously obtain spectral and photometric information of the targets, and tackle the science questions presented in this paper.