We aim to identify and demonstrate at least one new natural and precisely mathematically defined solution to the quantum reality (aka measurement) problem - i.e. a mathematical structure respecting Lorentz invariance and other symmetries that can sensibly be identified with an objective physical reality in a way that is demonstrably consistent with observed data. We aim further to characterize systematically the class of Lorentz invariant theories to which quantum theory belongs, to identify a much wider class of Lorentz invariant alternatives to quantum theory than previously known, and to identify new experimental tests of quantum theory ranging from terrestrial laboratory experiments through space-based experiments to cosmological tests. These results will build on a considerable body of published work by the PI and colleagues, together with as yet unpublished work, developed over many years. The results will be published in major peer reviewed journals and will form the core output. We will pursue these projects by extensive discussion and collaboration within the project team and with colleagues worldwide, supported by a postdoctoral researcher employed by the project. The project should have an enduring impact by making key scientific advances that change our understanding of the quantum reality problem and quantum theory, lead to new tests of quantum theory, and to new theoretical and experimental links between quantum foundations and cosmology.