An Analysis of Theories of Multiple Spin-2 Fields

Until recently, no consistent theory of more than two interacting spin-2 fields was known, except for a collection of pairwise bimetric couplings. In 2018, Hassan and Schmidt-May presented a theory with couplings beyond pairwise for an arbitrary number of fields in terms of vielbeins [1]. This theory was proved to propagate the correct number of modes and is hence free of the Boulware-Deser ghost. The spin-2 fields are represented by vielbein in this theory, but vielbeins are not the minimal covariant description of spin-2 fields, and they contain non-physical Lorentz degrees of freedom. Metrics provide a more familiar and natural representation of spin-2 fields, and in this thesis, such a formulation of the theory is presented. Though a formal proof of the absence of ghost modes in the metric formulations remains to be formulated, it is argued to be the first consistent multimetric theory beyond pairwise coupling. In this thesis, the known consistent theories of spin-2 fields are reviewed, in both the metric and vielbein formulation. The revision is preceded by the construction of a metric formulation of the new multivielbein theory. Multiple methods for expressing the theory in terms of metric are presented, and both the vielbein and metric field equations are derived and analysed. The equations of motion of the non-physical degrees of freedom are shown to give rise to constraints on the physical fields. These constraints are interpreted and solved, both numerically and analytically to conclude that non-trivial metric configurations exist. The constraints of both the new and previously known pairwise metric coupling are geometrically analysed in terms of overlapping null cones. The pairwise coupling is shown to allow overlaps that might give rise to undesired causal properties which do not seem to occur in the more general multimetric theory