Hermitian formulation for mass dimension one fermions: Flat and curved space-times

Throughout this paper, we conduct our discussion by a partial review of Elko's Hermiticity, introducing the Hermitian formulation for interacting mass dimension one fermions based on Elko spinor. It includes pivotal observations about renormalizability and the study of some allowed interactions. Beyond these points, since dark-matter phenomenology is mainly connected to gravitation, we introduce original remarks on how the Hermitian prescription can be readily generalized to include curved space-time, considering the very definition of the Elko spinor structure. We establish the Elko dual as arising from the path-integral formulation of a more fundamental structure. It enables one to include a curved background space-time and also quantum gravity into our investigations.