Decay of Oscillating Universes - Mithani, Audrey. (2017)
Abstract: It has been suggested by Ellis {et al} \cite{EM2004,Murugan} that the universe could be eternal in the past, without beginning. In their model, the ``emergent universe'' exists forever in the past, in an ``eternal'' phase before inflation begins. We will show that in general, such an ``eternal'' phase is not possible, because of an instability due to quantum tunneling. One candidate model, the ``simple harmonic universe'' has been shown by Graham {et al} \cite{Graham} to be perturbatively stable; we find that it is unstable with respect to quantum tunneling. We also investigate the stability of a distinct oscillating model in loop quantum cosmology with respect to small perturbations and to quantum collapse. We find that the model has perturbatively stable and unstable solutions, with both types of solutions occupying significant regions of the parameter space. All solutions are unstable with respect to collapse by quantum tunneling to zero size. In addition, we investigate the effect of vacuum corrections, due to the trace anomaly and the Casimir effect, on the stability of an oscillating universe with respect to decay by tunneling to the singularity. We find that these corrections do not generally stabilize an oscillating universe. Finally, we determine the decay rate of the oscillating universe. Although the wave function of the universe lacks explicit time dependence in canonical quantum cosmology, time evolution may be present implicitly through the semiclassical superspace variables, which themselves depend on time in classical dynamics. Here, we apply this approach to the simple harmonic universe, by extending the model to include a massless, minimally coupled scalar field $φ$ which has little effect on the dynamics but can play the role of a ``clock''.; Thesis (Ph.D.)--Tufts University, 2016.; Submitted to the Dept. of Physics.; Advisor: Alexander Vilenkin.; Committee: Krzysztof Sliwa, Jaume Garriga, Ken Olum, and Lawrence Ford.; Keywords: Physics, Theoretical physics, and Astrophysics.