一种用于德西特广义相对论的一阶规范方法
A First-Order Gauge Approach to de Sitter General Relativity
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中文总结 AI 辅助
该研究提出德西特相对论的一阶规范表述，将伪半径l(x)提升为时空场致SO(4,1)局部破缺。通过伊诺努 - 维格纳收缩等方法得出相关向量、能量 - 动量流等，证明场方程等价性，表明Λ(x)是时空挠率源，重述宇宙学常数问题。
中文摘要 AI 辅助
我们提出了一种德西特相对论的一阶规范表述，其中伪半径l(x)被提升为一个时空场，局部地将SO(4,1)破缺为SO(3,1)。这里，l(x)是一个几何补偿器，dl(x)是相关的序参量。这修改了强等效原理：局部真空跟随物质分布而非保持固定，同时广义相对论的传播自由度不变。在固定l(x)时，作用量是SO(3,1)规范不变的，但改变l(x)会破坏SO(4,1)全平移部分下的协变性。通过伊诺努 - 维格纳收缩，抽象生成元变为明确的时空变换，在宏观l趋于无穷和微观l趋于0的极限下产生非线性克利福德向量。广义诺特定理给出了一个统一的能量 - 动量流，将标准张量与适当的共形物质流耦合。没有物质时它恒为零，导致局部真空能量的渐近消失以及背景向闵可夫斯基时空的衰变。独立变分产生耦合的德西特场方程，我们代数地证明了它们与坐标流形上的张量分裂等价。规范比安基恒等式进一步表明Λ(x)是时空挠率的内在源，将其与对称破缺的局部序参量一致地识别。因此，宇宙学常数问题被重新表述，而非数值求解：从早期宇宙密度推导Λ(x)到其观测值的衰变仍是未来工作。
英文摘要
We propose a first-order gauge formulation of de Sitter relativity in which the pseudo-radius l(x) is promoted to a spacetime field, locally breaking SO(4,1) to SO(3,1). Here, l(x) is a geometric compensator and dl(x) the associated order parameter. This modifies the Strong Equivalence Principle: the local vacuum follows the matter distribution instead of remaining fixed, while the propagating degrees of freedom of General Relativity are unchanged. At fixed l(x), the action is SO(3,1)-gauge invariant, but varying l(x) destroys covariance under the full translational sector of SO(4,1). Through the Inonu-Wigner contraction, abstract generators become explicit spacetime transformations, yielding nonlinear Killing vectors in both the macroscopic l tends to infinity and microscopic l tends to 0 limits. The generalized Noether theorem gives a unified energy-momentum current coupling the standard tensor to the proper conformal matter current. It vanishes identically without matter, causing the asymptotic extinction of local vacuum energy and the decay of the background to Minkowski spacetime. Independent variations yield the coupled de Sitter field equations, and we algebraically prove their equivalence to the tensorial splitting on the coordinate manifold. Gauge Bianchi identities further show that Lambda(x) is an intrinsic source of spacetime torsion, consistently identifying it with the local order parameter of the symmetry breaking. The cosmological constant problem is therefore recast, not numerically solved: deriving the decay of Lambda(x) from early-universe densities to its observed value remains future work.
