https://doi.org/10.1140/epjc/s10052-021-09578-8
Regular Article - Theoretical Physics
Commutatively deformed general relativity: foundations, cosmology, and experimental tests
SWK Research, 1438 Chuckanut Crest Dr., 98229, Bellingham, WA, USA
a
Paul.deVegvar@post.harvard.edu
Received:
31
December
2020
Accepted:
26
August
2021
Published online:
5
September
2021
An integral kernel representation for the commutative 
-product on curved classical spacetime is introduced. Its convergence conditions and relationship to a Drin’feld differential twist are established. A -Einstein field equation can be obtained, provided the matter-based twist’s vector generators are fixed to self-consistent values during the variation in order to maintain -associativity. Variations not of this type are non-viable as classical field theories. -Gauge theory on such a spacetime can be developed using -Ehresmann connections. While the theory preserves Lorentz invariance and background independence, the standard ADM 
decomposition of 4-diffs in general relativity breaks down, leading to different -constraints. No photon or graviton ghosts are found on -Minkowski spacetime. -Friedmann equations are derived and solved for -FLRW cosmologies. Big Bang Nucleosynthesis restricts expressions for the twist generators. Allowed generators can be constructed which account for dark matter as arising from a twist producing non-standard model matter field. The theory also provides a robust qualitative explanation for the matter-antimatter asymmetry of the observable Universe. Particle exchange quantum statistics encounters thresholded modifications due to violations of the cluster decomposition principle on the nonlocality length scale 
. Precision Hughes–Drever measurements of spacetime anisotropy appear as the most promising experimental route to test deformed general relativity.
© The Author(s) 2021
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