标题： 可交换性变形广义相对论：基础、宇宙学与实验检验 显示英文标题

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

摘要： 对于弯曲经典时空上的交换$\star$-乘积，引入了一种积分核表示。其收敛条件和与Drin'feld微分扭结的关系得到了确立。如果在变化过程中将基于物质的扭结的矢量生成元固定为自洽值，以保持$\star$-结合性，则可以获得$\star$-爱因斯坦场方程。此类以外的变化在经典场论中不可行。可以使用$\star$-Ehresmann连接在这样的时空中发展$\star$-规范理论。虽然该理论保持了洛伦兹不变性和背景独立性，但广义相对论中4-微分的的标准 ADM$3+1$分解失效，导致不同的$\star$-约束。 在$\star$-闵可夫斯基时空上未发现光子或引力子的鬼粒子。 $\star$-弗里德曼方程被推导并求解用于$\star$-FLRW宇宙学。 大爆炸核合成限制了旋量生成器的表达式。 可以构造允许的生成器，这些生成器解释暗物质来源于产生非标准模型物质场的旋量。 该理论还为可观测宇宙的物质-反物质不对称性提供了稳健的定性解释。 粒子交换量子统计由于在非局域长度尺度$\sim10^{3-5} \,L_P$上违反了集团分解原理而出现\emph{阈值化}修改。 精确的休斯-德雷弗时空各向异性测量似乎是最有希望的实验途径来检验变形广义相对论。 显示英文摘要

摘要： 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 $3+1$ 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 \emph{thresholded} modifications due to violations of the cluster decomposition principle on the nonlocality length scale $\sim10^{3-5} \,L_P$. Precision Hughes-Drever measurements of spacetime anisotropy appear as the most promising experimental route to test deformed general relativity.