The Universe at Extreme Scales

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Research in particle physics and cosmology connects the largest scales, those of the Universe as a whole, with then smallest, namely those of fundamental particles. By trying to understand how the Universe evolved after the Big Bang, we may gain insight into which particles are yet to be discovered, e.g. at the Large Hadron Collider (LHC), and vice versa.Concerning the early Universe, it is commonly understood that it underwent a period of rapid expansion, called inflation. However, many open questions remain. For instance, what is the mechanism of cosmological inflation, and, can we linkinflation to quantum gravity, a theory that still eludes us? Interestingly, the recent observations of gravitational waves mayprovide a guide here. Inflation predicts a gravitational-wave background with properties depending on the details of theinflationary model. Hence if this background is observed, it may help us to further uncover details of the inflationary epochafter the Big Bang. Gravitational waves may also shed light on other puzzles, namely those related to dark energy and darkmatter. Again, possible alternative theories to Einstein's general theory of gravity, which are designed to solve the dark energy/matter puzzles, may leave their imprint in gravitational waves.In contrast to this, the LHC probes the smallest length scales, by colliding protons and nuclei at very high energies. In order to test the Standard Model (SM), our current highly successful theory of elementary particles, to the extreme, it is necessary to compute SM processes to high precision, and make predictions of physics beyond the Standard Model(BSM). The former can be done using advanced techniques which go beyond the usual Feynman diagrams. For the latter, one may take the viewpoint that the SM is an effective field theory (EFT), valid up to a certain energy scale only. To understand which novel BSM interactions can give rise to the SM at low energies, without conflicting with high-precisionfrom the LHC, is an outstanding challenge. Two main classes of candidate theories are so-called near-conformalgauge theories and Composite Higgs models, which both give rise to electroweak symmetry breaking and a light Higgs boson. They may even provide dark matter candidates.These theories have a commonality with the theory of quarks and gluons, Quantum Chromodynamics (QCD), namely that they are strongly interacting. This implies that they cannot be solved easily analytically, but are amenable to numerical simulations on high-performance computing facilities. The study of QCD provides a link between the physics of the earlyUniverse and elementary particles. Namely, as the Universe cooled down after the Big Bang, it underwent a series ofphase transitions. During one of those, quarks and gluons combined into hadrons, i.e. the particles we observe today. TheQCD phase transition is currently being explored at the LHC, by colliding heavy ions, motivating quantitative predictions onhow the QCD spectrum changes with temperature. In fact, even understanding the QCD spectrum in vacuum is still partly unsolved and may guide toward BSM physics.Quantum field theories (QFTs) describes physical processes across a vast range of energy scales, from fundamental interactions, as mentioned above, to low-dimensional and condensed matter systems. Many new phenomena and the detailed structure of QFTs are anticipated to lie beyond the confines of traditional perturbative methods or numericalsimulations. Dualities provide links between hitherto unrelated theories, making tractable questions previously consideredto be out of reach. With new dualities being discovered, the richness of QFT is larger than naively expected. Similarly,dynamics out of thermal equilibrium, the process of thermalisation, or the evolution of quantum information, relevant forblack hole dynamics, benefits from new approaches, some of which are motivated by quantum information.