One of the great puzzles in modern physics and cosmology concerns the origin of dark energy. It has been discovered in 1998, that our Universe expands currently at an accelerating rate. As a prominent explanation, the existence of an unknown substance, called dark energy, that fills the Universe has been postulated. A theoretical description of dark energy is naturally given by new hypothetical scalar fields, which couple to gravity. Despite intensive efforts, no scalar fields have been discovered by observations at solar or terrestrial scales. A complementary search for such hypothetical new scalar fields is possible by employing high precision tabletop experiments. This proposal is a follow-up project to FWF P 34240-N and significantly extends and improves the previous theoretical analysis for the detection of dark energy models with these experiments. This enables also to search for dark energy by new novel means. For the practical realization of the aims of this project methods will be used that have been employed and developed by our working group previously, especially in the previous project FWF P 34240-N. For the analysis of dark energy models well established methods of (quantum) field theory including a mixture of analytical as well as numerical methods will be adapted and further developed. So far the true origin of dark energy is completely unknown and certainly constitutes one of the most important tasks that confronts physicists as well as cosmologists in our time. Complementary to searches with colliders and cosmological observations is the search employing high-precision tabletop experiments. As has been revealed in the previous project FWF P 34240-N, each tabletop experiment has a complementary sensitivity for different dark energy models stressing the importance of employing a host of several experiments. A direct result of this collaboration has lead to a new neutron interferometer experiment that is currently setup at ILL. In this follow-up project the necessary theoretical analysis for these tabletop experiments will be provided. The previously employed theoretical tools will be significantly extended and further developed, which enables also to explore dark energy by new novel means. The principal investigator, Mario Pitschmann, has experience in all areas relevant for successfully carrying out the aims of this research project. He will be funded by the TU Wien. The PostDoc Chad J. Briddon is an expert on scalar fields that arise in the contexts of dark energy and modified gravity theories. Further support for this project should be provided by the PhD student Caroline Voith, who has acquired the necessary background in scalar fields and quantum field theory during her master thesis under the supervision of the principal investigator.