Partially Massless Spin 2 Electrodynamics

Abstract

We propose that maximal depth, partially massless, higher spin excitations can mediate charged matter interactions in a de Sitter universe. The proposal is motivated by similarities between these theories and their traditional Maxwell counterpart: their propagation is lightlike and corresponds to the same Laplacian eigenmodes as the de Sitter photon; they are conformal in four dimensions; their gauge invariance has a single scalar parameter and actions can be expressed as squares of single derivative curvature tensors. We examine this proposal in detail for its simplest spin 2 example. We find that it is possible to construct a natural and consistent interaction scheme to conserved vector electromagnetic currents primarily coupled to the helicity 1 partially massless modes. The resulting current-current single ``partial-photon'' exchange amplitude is the (very unCoulombic) sum of contact and shorter-range terms, so the partial photon cannot replace the traditional one, but rather modifies short range electromagnetic interactions. We also write the gauge invariant fourth-derivative effective actions that might appear as effective corrections to the model, and their contributions to the tree amplitude are also obtained.