On the Cauchy problem for Weyl-geometric scalar-tensor theories of gravity

In this paper, we analyze the well-posedness of the initial value formulation for particular kinds of geometric scalar-tensor theories of gravity, which are based on aWeyl integrable space-time. We will show that, within a frame-invariant interpretation for the theory, the Cauchy problem in a vacuum is well-posed. We will analyze the global in space problem, and, furthermore, we will show that geometric uniqueness holds for the solutions. We make contact with Brans-Dicke theory, and by analyzing the similarities with such models, we highlight how some of our results can be translated to this well-known context, where not all of these problems have been previously addressed. Published by AIP Publishing.