Geodesic Scattering and Lorentz Invariance in Stochastic Gravity

Abstract: Stochastic gravity opens up the ability to study problems where quantum fluctuations are important in semiclassical gravity. Many of these problems require regularization techniques which may break certain symmetries. In this thesis, the effects of fluctuating spacetime on geodesics is studied in the framework of interacting quantum field theories and in studying geodesic deviation. The possibility of using Pauli-Villars to regularize quantum fields in stochastic gravity calculations is explored. The scattering of geodesics is determined to be a small effect and not predicted in the framework of semiclassical or stochastic gravity. The study of geodesic deviation in interferometer experiments gives some indication that parametric resonance effects could have a significant role in stochastic gravity. The Pauli-Villars regularization scheme is shown to have significant problems when applied to stochastic gravity, such as failures in second-order stress-energy tensor terms and restrictions due to the kinematic properties of negative-norm fields.