Signatures of modified gravity from the gravitational Aharonov-Bohm effect

Abstract: To date, no observational confirmation of dark matter particles has been found. In this paper, we put forward an alternative approach to inferring evidence for dark matter through modified gravity, without invoking fundamental dark matter particles. Specifically, we explore the possibility of extracting signatures of Kaluza-Klein gravity through the gravitational Aharonov-Bohm effect. Kaluza-Klein theory has recently been proposed as an alternative to the dark sector, and predicts a tower of particles, including spin-0 and spin-1 gravitons alongside the usual spin-2 gravitons, which can gravitationally couple to matter. We thus analyze a quantum system in free fall around a gravitating body in the presence of a modified Yukawa-like gravitational potential, and determine the gravitational phase induced by the additional degrees of freedom introduced by the Kaluza-Klein model. Our results reveal that, in addition to the usual result from General Relativity, the quantum wave function of the system exhibits an additional effect: a splitting of the energy levels with a new quantum number due to the extra vector gravitational degrees of freedom. The energy splitting difference between general relativity and Kaluza-Klein gravity is found to be of the order of meV for an atomic system and eV for a nuclear system. Similar values also arise in generic modified gravity models and can be feasibly tested in the future. Numerical estimates for the graviton mass are also provided, and potential imprints on gravitational waves are mentioned.