Constructing Shape Dynamics in the BKL Scenario

Master's thesis at Perimeter Institute, supervised by Tim Koslowski

In this essay we construct shape dynamics explicitly for the BKL scenario. After a short review of symplectic geometry and classical systems with constraints, we explain how Shape Dynamics arises as an equivalent theory to general relativity with dierent gauge orbits. For this, we describe the construction of a linking theory that connects both theories. Having introduced this, we calculate the shape dynamics Hamiltonian for an homogeneous, anisotropic universe. Finally, we make the dictionary manifest which maps observables of general relativity and shape dynamics into each other. By doing so, we can circumvent important complications which usually arise from the Hamiltonian constraint when one tries to extract Dirac observables from general relativity.

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