Fields, Strings and Lattices: From the Inflationary Universe to High-Energy Colliders

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Research in particle physics and cosmology connects the largest scales, those of the Universe as a whole, with the smallest, namely those of fundamental particles and strings. By trying to understand how the Universe evolved after the Big Bang, we may gain insight into which particles are yet to be discovered at e.g. the Large Hadron Collider at CERN, and vice versa, a fascinating prospect!It is commonly assumed that the early Universe went through a period of rapid expansion, dubbed inflation. The mechanisms underlying inflation can be investigated in a number of ways. In the so-called bottom-up approach, one aims to find predictions that are independent of details of models, but only depend on symmetries and the nature of the source of inflation. It is then possible to extract universal features leading to observational predictions and point towards physics beyond our currently known Standard Models of Particle Physics and Cosmology. In the complementary top-down approach, one starts with the given theory, e.g. one that is motivated by string theory, and derives its consequences, which, again might be testable by observations. These approaches can also be used to study the period of cosmic acceleration our Universe is currently going through, i.e. dark energy.String theory is a theory of gravity (and other forces) operating at very high-energy scales. Besides its possible role as a fundamental theory, it has many intricate aspects which require a level of understanding deeply rooted in symmetries and dualities (a transformation that leads to two 'dual' formulations which are superficially very different but yet equivalent). By studying those, one may not only understand string theory better, but also arrive at dual theories which are relevant for e.g. physics beyond the Standard Model (BSM) probed at the LHC, especially if the BSM model is strongly coupled.In order to make predictions for the LHC, it is necessary to perform very precise calculations, in BSM models and in the Standard Model itself. Some of these calculations can be done by expanding in a small parameter. This does not mean that the computation is easy though, since many scattering processes may contribute. However, it might be that by re-organising these contributions a new, more efficient, formulation can be found.When there is no small parameter, a theory has to be solved as it stands. Often this can be attempted numerically, by formulating it on a space-time lattice. Since this involves very many degrees of freedom, typically one has to employ the largest supercomputers in the world. The theory of the strong interaction, Quantum Chromodynamics (QCD), is one of those theories in which a small parameter is absent. Although it is formulated in the terms of quarks (as matter particles) and gluons (as force carriers), these are not the particles that appear in the spectrum, which are instead protons, neutrons, pions etc. However, since QCD is so hard to solve, there may be other particles not yet detected and also not yet understood theoretically: examples are so-called glueballs and hybrid mesons. By studying QCD on the lattice, these ideas can be tested quantitatively.A related question concerns what happens with all these particles when the temperature (as in the early Universe) or the matter density (as in neutron stars) is increased. Also this can be studied numerically and a transition to a new phase of matter at high temperature, the quark-gluon plasma, has been observed. Since this phase is currently being explored at the LHC, by colliding heavy ions, quantitative predictions on the spectrum and on transport properties, such as how viscous the plasma is, are needed here as well. Some BSM models also lack a small parameter and hence are studied using similar lattice computing techniques. By scanning models with distinct features, again hints for the LHC may be found, e.g. with regard to unusual spectral features.