PhD Thesis Defenses

PhD Thesis defense: Constraints and symmetries in theories of interacting spin-2 fields

The Hassan-Rosen bimetric theory describes two interacting spin-2 fields, one massless and one massive. In this thesis, a complete canonical analysis of this theory is performed in the metric formulation and all constraints are computed. In particular, a secondary constraint, whose existence was in doubt, is shown to exist and evaluated explicitly, bringing the total number of constraints up to six. This, together with general covariance, is enough to eliminate the Boulware-Deser ghost and ensure that the theory propagates the appropriate seven degrees of freedom. The requirement that the constraints are preserved in time leads to a linear relation between the lapse functions of the two metrics. Knowing the explicit form of the ratio of the lapses is necessary for solving initial value problems. The ratio is computed for the special case where the metrics share the same spherical symmetry. Since the bimetric theory is diffeomorphism invariant, it must contain four first class constraints whose Poisson brackets form a certain algebra. In general, it is possible to use this algebra to identify a metric. In this thesis, the four first class constraints of bimetric theory are identified and it is shown that their Poisson brackets indeed forms the algebra required by diffeomorphism invariance. However, the metric identified from the algebra turns out not to be unique, but to depend on a choice of variables. Additionally, it need not coincide with the gravitational metric. The candidate nonlinear partially massless bimetric theory is also investigated in this thesis. It is shown that for this theory, the partially massless symmetry cannot be extended beyond cubic order in the action. This result is generalized to the most general two derivative theory of only two interacting spin-2 fields, showing that such a theory cannot possess thepartially massless symmetry beyond cubic order.