This page lists a few ideas and suggestions for possible thesis topics which I offer to supervise. Also other topics in the general field of geometry, gravity, its mathematical foundations and phenomenology are possible. A limited amount of funding for students is available.
The basic idea of multimetric gravity is the assumption that dark matter and dark energy effects are caused by additional, "dark" copies of the standard model, each of which couples to its own metric, and which interact with the visible standard model matter only via repulsive gravity. It has been shown that this assumption may indeed lead to an accelerating cosmology, while being cosistent with solar system observations. The derived cosmological solution has the property that all metrics become the same, and are of Robertson-Walker type with identical scale factors. The student's central task is to figure out whether this solution is stable with respect to small, non-symmetric perturbations of the scale factors. For this purpose it is necessary to derive the equations of motion for these perturbations in a linear approximation. From these equations one may then derive the time evolution of the perturbations and determine whether they grow, leading to an unstable solution, or shrink, so that they converge to a stable cosmological solution.
An important formalism for testing metric based gravity theories is the parameterized post-Newtonian (PPN) formalism. It allows to characterise any given gravity theory by a set of ten parameters, whose values have been measured to high precision in various solar system experiments. Any viable gravity theory must satisfy the bounds obtained from these experiments. The student's task is to determine the PPN parameters for a particular metric gravity theory, which may be more or less freely chosen, and to compare the result with solar system constraints.