Classically Consistent Theories of Interacting Spin-2 Fields

Sammanfattning: This doctoral thesis comprises a study of recently developed nonlinear theories for massive spin-2 fields that go by the names of Massive Gravity and Bimetric Theory. As we demonstrate in a Hamiltonian analysis, the construction of these theories avoids the notorious Boulware-Deser ghost instability that generically plagues nonlinear spin-2 interactions and renders their description inconsistent. We explore the mass spectrum of ghost-free Bimetric Theory and reformulate its action in terms of nonlinear mass eigenstates. A generalized version of the theory with multiple vielbein interactions is reviewed and then reexpressed in terms of metrics. Homogeneous and isotropic solutions to the equations of motion in Bimetric Theory are derived and discussed in the context of cosmology. We furthermore single out particular values for the parameters in the bimetric interaction potential for which the theory could potentially contain an additional gauge redundancy. This establishes a unique candidate for a nonlinear theory of a partially massless spin-2 field. Finally, we reveal a close connection of Bimetric Theory to a certain class of higher-curvature theories for gravity and offer a solution to their ghost problems. In particular we find that, in four space-time dimensions, the bimetric candidate for nonlinear partial masslessness is closely related to Conformal Gravity.