Cosmology models the behaviour of our universe in terms of a small set of descriptive variables; the scale factor, Hubble parameter, relative shear expansions etc. From Einstein’s equations we can calculate the equations of motion of these systems and find their evolution. The complete behaviour can be described in terms of dynamical systems arising from a Hamiltonian and expressed as a flow on phase space. All these descriptions rely upon factors which cannot be explicitly measured by an observer within the universe at all times. In recent work I have shown that under certain conditions these can be extended beyond the initial singularity. One key aspect of your project will be to examine the nature of singularities in relational systems.
The goal of this project will be to develop a complete description of cosmological systems which relies only upon relational measurements, and find their cosmological completions. You will develop skills in differential geometry (particularly symplectic geometry) and numerical methods alongside a strong understanding of physical systems. You will gain significant insight into the nature of singularities in general relativity and the geometry of mathematical physics.
The Physics Department is holder of an Athena SWAN Silver award and JUNO Championship status and is strongly committed to fostering diversity within its community as a source of excellence, cultural enrichment, and social strength. We welcome those who would contribute to the further diversification of our department.