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An integral kernel representation for the commutative $\star$-product oncurved classical spacetime is introduced. Its convergence conditions andrelationship to a Drin'feld differential twist are established. A$\star$-Einstein field equation can be obtained, provided the matter-basedtwist's vector generators are fixed to self-consistent values during thevariation in order to maintain $\star$-associativity. Variations not of thistype are non-viable as classical field theories. $\star$-Gauge theory on such aspacetime can be developed using $\star$-Ehresmann connections. While thetheory preserves Lorentz invariance and background independence, the standardADM $3+1$ decomposition of 4-diffs in general relativity breaks down, leadingto different $\star$-constraints. No photon or graviton ghosts are found on$\star$-Minkowski spacetime. $\star$-Friedmann equations are derived and solvedfor $\star$-FLRW cosmologies. Big Bang Nucleosynthesis restricts expressionsfor the twist generators. Allowed generators can be constructed which accountfor dark matter as arising from a twist producing non-standard model matterfield. The theory also provides a robust qualitative explanation for thematter-antimatter asymmetry of the observable Universe. Particle exchangequantum statistics encounters \emph{thresholded} modifications due toviolations of the cluster decomposition principle on the nonlocality lengthscale $\sim10^{3-5} \,L_P$. Precision Hughes-Drever measurements of spacetimeanisotropy appear as the most promising experimental route to test deformedgeneral relativity.

Commutatively Deformed General Relativity: Foundations, Cosmology, and Experimental Tests