Cyclic universes & direct detection of cosmic expansion by holonomy in the McVittie spacetime - Campbell, Mariam (Department of Maths and Applied Maths, 2020)
This dissertation consists of two parts. They are separate ideas, but both fall into the context of General Relativity using dynamical systems. Part one is titled Cyclic Universes. It is shown that a Friedmann model with positive spatial sections and a decaying dark energy term admits cyclic solutions which is shown graphically by the use of phase planes. Coupling the modified Friedmann model to a scalar field model with cross-sectional terms in order to model the reheating phase in the early universe, it is found that there is a violation of the energy condition, i.e. when the universe is in the contracting phase and re-collapses again. We suspect that the cause for this violation is due to the asymmetry of the solution of w together with the cross-sectional terms at the bounce preceding slow-roll inflation. Part two is titled Thought Experiment to Directly Detect Cosmic Expansion by Holonomy. Two thought experiments are proposed to directly measure the expansion of the universe by the parallel transfer of a vector around a closed loop in a curved spacetime. Generally, expansion would cause a measurable deficit angle between the vector’s initial and final positions. Using the McVittie spacetime (which describes a spherically symmetric object in an expanding universe) as a backdrop to perform these experiments it is shown that the expansion of the universe can be directly detected by measuring changes in the components of a gyroscopic spin axis. We find these changes to be small but large enough (∆S ∼ 10−7 ) to be measured if the McVittie spacetime were a representation of our universe.