Constraints on short-range modified gravity with self-gravitating Bose-Einstein condensates

Theories of modified gravity often predict deviations from Newton's law of gravitation. In many cases these deviations are parametrised in the form of a Yukawa potential which introduces two Yukawa parameters: The interaction strength and the effective interaction range. For both parameters upper constraints have been found by a variety of experiments covering distances of more than thirdy orders of magnitude.

In order to improve the constraints especially in the submicrometer regime, we introduce in this thesis a novel theoretical concept. We consider a quantum mechanical many-particle system, a so-called self-gravitating Bose-Einstein condensate, in which the individual particles interact additionally via a gravitational potential. Our model therefore differs from previous tests, which mostly refer to external gravitational fields. To ensure experimental testability, we study the collective frequencies of such a condensate, which are known to depend on the intrinsic interaction. Using a variational method, we analytically determine step by step the contributions to the collective frequencies due to the contact interaction, a Newtonian and a Yukawa-like interaction. Furthermore, we also consider spherical and axially symmetric condensates, where the latter can be realised in cigar-shaped or disk-shaped form.