  Despite their tremendous successes, modern-day cosmology and particle physics
harbor a variety of unresolved mysteries. Two of the biggest are the origin of
the baryon asymmetry of the Universe and the existence and nature of dark
matter. In the present thesis, the author addresses these topics in various
ways. The first part of the thesis is concerned with cosmological first-order
phase transitions that may have occurred shortly after the Big Bang. Such
transitions proceed via the nucleation and expansion of true vacuum bubbles and
give rise to a rich phenomenology. The author suggests a mechanism to
simultaneously explain the baryon asymmetry and dark matter, based on the
out-of-equilibrium dynamics at the boundary of a dark phase transition with
large order parameter. The same class of phase transitions can, in the
parameter regime of small dark matter Yukawa couplings, lead to the production
of primordial black holes via the compression of the plasma in shrinking false
vacuum regions, as the author demonstrates with a sophisticated numerical
simulation. In a third project regarding cosmological phase transitions, the
author investigates the possibility of sub-MeV hidden sectors that are
decoupled from the remaining plasma and cold enough to be reconciled with
cosmological constraints, but at the same time give rise to a detectable
gravitational-wave spectrum produced during bubble collisions. In the second
part of the thesis, the author assesses the prospects for new physics searches
at the DUNE near detector, focusing on the DUNE-PRISM concept, which suggests
consecutive measurements at different on- and off-axis positions. This setup
achieves improved signal-to-background ratios and reduces systematic
uncertainties.
