Institut für Physik und Astronomie
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Recent astronomical data strongly suggest that a significant part of the dark matter content of the Local Group and Virgo Supercluster is not incorporated into the galaxy halos and forms diffuse components of these galaxy clusters. A portion of the particles from these components may penetrate the Milky Way and make an extragalactic contribution to the total dark matter containment of our Galaxy. We find that the particles of the diffuse component of the Local Group are apt to contribute similar to 12% to the total dark matter density near Earth. The particles of the extragalactic dark matter stand out because of their high speed (similar to 600 km s(-1)), i.e., they are much faster than the galactic dark matter. In addition, their speed distribution is very narrow (similar to 20 km s(-1)). The particles have an isotropic velocity distribution (perhaps, in contrast to the galactic dark matter). The extragalactic dark matter should provide a significant contribution to the direct detection signal. If the detector is sensitive only to the fast particles (v > 450 km s(-1)), then the signal may even dominate. The density of other possible types of the extragalactic dark matter (for instance, of the diffuse component of the Virgo Supercluster) should be relatively small and comparable with the average dark matter density of the universe. However, these particles can generate anomaly high-energy collisions in direct dark matter detectors.
Famously, Einstein read off the geometry of spacetime from Maxwell's equations. Today, we take this geometry that serious that our fundamental theory of matter, the standard model of particle physics, is based on it. However, it seems that there is a gap in our understanding if it comes to the physics outside of the solar system. Independent surveys show that we need concepts like dark matter and dark energy to make our models fit with the observations. But these concepts do not fit in the standard model of particle physics. To overcome this problem, at least, we have to be open to matter fields with kinematics and dynamics beyond the standard model. But these matter fields might then very well correspond to different spacetime geometries. This is the basis of this thesis: it studies the underlying spacetime geometries and ventures into the quantization of those matter fields independently of any background geometry. In the first part of this thesis, conditions are identified that a general tensorial geometry must fulfill to serve as a viable spacetime structure. Kinematics of massless and massive point particles on such geometries are introduced and the physical implications are investigated. Additionally, field equations for massive matter fields are constructed like for example a modified Dirac equation. In the second part, a background independent formulation of quantum field theory, the general boundary formulation, is reviewed. The general boundary formulation is then applied to the Unruh effect as a testing ground and first attempts are made to quantize massive matter fields on tensorial spacetimes.