Towards a relativity of dark-matter rods and clocks

TL;DR

This paper explores how dark matter, specifically Elko particles, could cause deviations in gravitational behavior from standard general relativity, especially at the interface between dark matter and ordinary matter, due to differences in their fundamental structures.

Contribution

It introduces the idea that dark matter rods and clocks may have different algebraic structures, leading to potential deviations in gravity predictions within the dark sector and at dark-visible matter interfaces.

Findings

Dark matter rods and clocks may not share the same algebraic structure as standard model ones.

Gravity effects in the dark sector could deviate from general relativity predictions.

Effects depend on the angular momentum and spin of the gravitational environment.

Abstract

In the absence of dark matter, the dynamical and kinematical interpretations of the special relativistic spacetime have been and still are the topic of philosophic debate, which whilst fertile, is by and large of little predictive power. This changes dramatically if the debate includes a dark matter candidate in a "non-trivial" extension of the standard model. Here I argue that rods and clocks made out of dark matter may not reveal the same underlying algebraic structure as the rods and clocks made out of standard model particles. For the sake of concreteness I here exemplify the argument by looking at a particular dark matter candidate called Elko. Inevitably, one is led to the conclusion that gravity within the dark sector, and at the interface between dark matter and standard-model matter, may deviate from the canonical general relativistic predictions. For Elko dark matter such effects will be of second order in the sense that they will depend only on the angular momentum and spin of the gravitational environment.