Constructing Shape Dynamics in the BKL Scenario

Master's Defense, Perimeter Institute for Theoretical Physics

After a short review of symplectic geometry and classical systems with constraints, I will explain how Shape Dynamics arises as an equivalent theory to general relativity with dierent gauge orbits. For this, I describe the construction of a linking theory that connects both theories. Having introduced this, I review my calculations of the shape dynamics Hamiltonian for an homogeneous, anisotropic universe. I will show how the dictionary becomes manifest and maps observables of general relativity and shape dynamics into each other. This allows to circumvent important complications which usually arise from the Hamiltonian constraint when one tries to extract Dirac observables from general relativity.