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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.