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 ∼1−10 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.Comment: 47 pages including references, 0 figures, 0 tables Various
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