Exotic Dark Spinor Fields

TL;DR

This paper explores exotic dark spinor fields in curved spacetimes, revealing how their unique properties can probe spacetime topology and metric structure, with implications for dark matter research.

Contribution

It introduces and analyzes exotic dark spinor fields, highlighting their potential to detect non-trivial spacetime topologies and their distinct behavior compared to other spinor fields.

Findings

Exotic dark spinor fields cannot hide their topological terms due to lack of electromagnetic charge.

Such fields can impose constraints on spacetime topology through their dynamics.

Dark spinor fields are promising candidates for dark matter and spacetime topology probes.

Abstract

Exotic dark spinor fields are introduced and 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 Cech cohomology class. For the most kinds of spinor fields, any exotic term in the Dirac operator can be absorbed and encoded as a shift of the electromagnetic vector potential representing an element of the cohomology group H^1(M, Z_2). The possibility of concealing such an exotic term does not exist in case of dark (ELKO) spinor fields, as they cannot carry electromagnetic charge, so that the full topological analysis must be evaluated. 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 calculated. It forthwith implies that the non-trivial topology associated to the spacetime can drastically engender --- from the dynamics of dark spinor fields --- constraints in the spacetime metric structure. Meanwhile, such constraints may be alleviated, at the cost of constraining the exotic spacetime topology. Besides being prime 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 probe the spacetime metric structure.