Very special relativity as relativity of dark matter: the Elko connection

TL;DR

This paper proposes that very special relativity (VSR) operates in the dark sector at energies similar to the standard model, introducing a new spinor field related to Elko that is invariant under VSR and exhibits intrinsic darkness.

Contribution

It constructs a VSR-invariant spinor field akin to Elko, resolving the tension between Elko and Lorentz symmetries and suggesting VSR's role in dark matter physics.

Findings

Introduces a VSR-invariant spinor field similar to Elko.

Shows the dark sector may obey VSR instead of Lorentz symmetry.

Resolves the Lorentz symmetry tension in Elko theories.

Abstract

In the very special relativity (VSR) proposal by Cohen and Glashow, it was pointed out that invariance under HOM(2) is both necessary and sufficient to explain the null result of the Michelson-Morely experiment. It is the quantum field theoretic demand of locality, or the requirement of P, T, CP, or CT invariance, that makes invariance under the Lorentz group a necessity. Originally it was conjectured that VSR operates at the Planck scale; we propose that the natural arena for VSR is at energies similar to the standard model, but in the dark sector. To this end we provide an ab initio spinor representation invariant under the SIM(2) avatar of VSR and construct a mass dimension one fermionic quantum field of spin one half. This field turns out to be a very close sibling of Elko and it exhibits the same striking property of intrinsic darkness with respect to the standard model fields. In the new construct, the tension between Elko and Lorentz symmetries is fully resolved. We thus entertain the possibility that the symmetries underlying the standard model matter and gauge fields are those of Lorentz, while the event space underlying the dark matter and the dark gauge fields supports the algebraic structure underlying VSR.