Gravitational Faraday Effect induced by Dark Matter Spin

TL;DR

This paper predicts a gravitational Faraday effect caused by dark matter spin, leading to polarization rotation of gravitational waves, with potential implications for early universe cosmology.

Contribution

It introduces a novel gravitational Faraday effect induced by dark matter spin and provides an expression for the rotation angle in astrophysical contexts.

Findings

The effect is likely small under current constraints.

The effect could be significant in the early universe.

A formula for the gravitational rotation angle is derived.

Abstract

We show that the spin of dark matter induces a gravitational analog of the electromagnetic Faraday effect, where the polarization of gravitational waves undergoes a rotation as they propagate through a dark matter halo with a non-vanishing axial spin tensor (hypermomentum). An expression for the gravitational rotation angle is provided, which is analogous to the Faraday rotation in optics, and evaluate its significance in astrophysical settings. Although the effect is expected to be small under current observational constraints, we discuss its potential importance in the early universe.