Final Activity Report Summary - RELATIVITY TESTS (Studies of Quantum-Gravitational Relativity Violations) Present-day physics rests on two equally important cornerstones, namely the quantum theory, which primarily describes the microscopic world of atoms and particles, and gravity, which governs macroscopic physics, such as the motion of planets and the evolution of the universe. A key goal in contemporary physics is to combine these two cornerstones into a single unified theory. Various theoretical approaches along these lines suggest that this requires minuscule departures from Einstein's relativity theory. This project was concerned with the theoretical description of such putative relativity violations, as well as with the identification of suitable experiments that could test these ideas and the following results were obtained. In the context of the Standard model extension (SME), which is the customary framework for the theoretical description of such effects, various mathematical investigations were performed. These studies yielded valuable insight into the SME and provided tools for simplifying SME calculations. One particular study led to the construction of the first locality-preserving model within a recent approach to relativity violations called very special relativity. In the context of predicting effects for experimental tests, a method was developed to employ high-energy particle colliders to constrain certain types of relativity violations. In particular, observations made at the large electron-positron collider at the European Organisation for Nuclear Research (CERN) and at the Tevatron at Fermilab improved previous experimental results by three to four orders of magnitude. The mathematical description of relativity violations in the SME framework shared many similarities with conventional physics in the presence of an external medium, e.g. light inside a crystal. Various theoretical methods originally developed for the SME could therefore also be applied to ordinary physics in situations involving external media. This idea was exploited to study the travel of neutrinos from the solar core to Earth. Such neutrinos could be generated by Dark matter (DM) annihilations in the Sun. The results of these studies were twofold. They could help to unravel the nature of DM and they might be used to determine presently unmeasured neutrino parameters.
