Unravelling Consistent Spin-2 Interactions

Sammanfattning: Recently, a unique formulation of a classically consistent theory of massive spin-2 fields has emerged. In this thesis I address a few of the primary questions that arise once such a theory is available.I will discuss cosmological solutions in a bimetric setup and show that, as far as the background evolution is concerned, a theory of interacting spin-2 fields remain a viable option to the mainstream ΛCDM concordance model. In general, the bimetric solutions are quite different from general relativistic solutions and hence in many situations will not be supported by observations. I highlight a particularly useful class of bimetric solutions which mimic general relativity exactly at the background level. This class of solutions is very special since it both uniquely provide the maximally symmetric vacuum solutions in the absence of matter sources as well as uniquely provide a massive Fierz-Pauli wave equation for perturbations of these backgrounds. This allow us a clear interpretation of the spectrum of perturbations in terms of mass eigenstates. I provide a nonlinear extension of these mass eigenstates into nonlinear fields which are not true mass eigenstates but still provide useful input into the theoretical understanding of the theory. These nonlinear extensions are particularly interesting both with respect to parameterizing generic deviations of the bimetric solutions to general relativistic solutions, as well as providing further insight into some unresolved questions related to ``massive gravity" in maximally symmetric backgrounds, such as the illusive nature of the Higuchi bound and its accompanying linear on-shell gauge invariance.The special structure of the consistent interacting theory provides the basic tool to start to unravel some of the mysteries connected with spin-2 fields, with hope to reinvestigate many fundamental open questions explicitly related to the gravitational sector of field theory.