Commutatively deformed general relativity: foundations, cosmology, and experimental tests

• Main Author: P. G. N. de Vegvar
• Format: Article
• Language: English
• Published: SpringerOpen 2021-09-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: https://doi.org/10.1140/epjc/s10052-021-09578-8

Abstract An integral kernel representation for the commutative $$\star $$ ⋆ -product on curved classical spacetime is introduced. Its convergence conditions and relationship to a Drin’feld differential twist are established. A $$\star $$ ⋆ -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 $$\star $$ ⋆ -associativity. Variations not of this type are non-viable as classical field theories. $$\star $$ ⋆ -Gauge theory on such a spacetime can be developed using $$\star $$ ⋆ -Ehresmann connections. While the theory preserves Lorentz invariance and background independence, the standard ADM $$3+1$$ 3 + 1 decomposition of 4-diffs in general relativity breaks down, leading to different $$\star $$ ⋆ -constraints. No photon or graviton ghosts are found on $$\star $$ ⋆ -Minkowski spacetime. $$\star $$ ⋆ -Friedmann equations are derived and solved for $$\star $$ ⋆ -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 $$\sim 10^{3-5} \,L_P$$ ∼ 10 3 - 5 L P . Precision Hughes–Drever measurements of spacetime anisotropy appear as the most promising experimental route to test deformed general relativity.