Commutative deformations of general relativity: nonlocality, causality, and dark matter

TL;DR

This paper explores how Drinfeld twists in deformed general relativity induce nonlocality and causality effects, proposing dark matter candidates and analyzing their experimental implications within a non-extended framework.

Contribution

It introduces a novel application of Hopf algebra methods to deformed general relativity, generating self-consistent twists and analyzing their physical consequences without extra dimensions or supersymmetry.

Findings

A classical nonlocality scale emerges above which microcausality is restored.

Deformed Maxwell equations predict negligible cosmological dispersion for photons.

Dark matter candidates arise from matter fields inducing twists, with minimal experimental effects.

Abstract

Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on \emph{commutative} manifolds. A classical nonlocality length scale is produced above which microcausality emerges. Matter fields are utilized to generate self-consistent Abelian Drinfeld twists in a background independent manner and their continuous and discrete symmetries are examined. There is negligible experimental effect on the standard model of particles. While baryonic twist producing matter would begin to behave acausally for rest masses above $\sim1-10$ TeV, other possibilities are viable dark matter candidates or a right handed neutrino. First order deformed Maxwell equations are derived and yield immeasurably small cosmological dispersion and produce a propagation horizon only for photons at or above Planck energies. This model incorporates dark matter without any appeal to extra dimensions, supersymmetry, strings, grand unified theories, mirror worlds, or modifications of Newtonian dynamics.