ELKO SPINOR FIELDS AS A TOOL FOR PROBING EXOTIC TOPOLOGICAL SPACETIME FEATURES

Abstract

We report about some achievements and developments provided by the ELKO program, in particular the ones recently accomplished.1 Exotic dark spinor fields has been investigated in the context of inequivalent spin structures on arbitrary curved spacetimes, which induces an additional term on the associated Dirac operator, related to a Čech cohomology class. Exotic terms operating on standard model Dirac spinor fields are usually absorbed by gauge transformations encoded as a shift of some vector potential representing an element of the cohomology group H1(M, ℤ2). That is not the case of ELKO, once they cannot carry gauge charge. As a consequence, the ELKO program requires a complete evaluation of topological analysis. Since exotic dark spinor fields also satisfy Klein-Gordon propagators, the dynamical constraints related to the exotic term in the Dirac equation can be explicitly computed. It forthwith implies that the non-trivial topology associated to the spacetime can drastically engender — from the dynamics of dark spinor fields — constraints on the spacetime metric structure. Besides being candidates to the dark matter problem, dark spinor fields are shown to be potential candidates to probe non-trivial topologies in spacetime, as well as to explain the spacetime metric structure.