发表机构
Queen Mary University of London; University of the Western Cape; National Institute for Theoretical & Computational Sciences（伦敦大学玛丽女王学院; 西开普大学; 理论与计算科学国家研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出协变动力学框架，以无碰撞气体替代尘埃模型，通过速度弥散处理流交叉，推导4-加速度和涡度，补全尘埃宇宙学并支持局部距离-红移数据检验。
AI 中文摘要
将冷暗物质建模为尘埃使得物质世界线为测地线，从而从局部哈勃流中移除了任何固有的偶极。尘埃模型在流交叉发展时失效，而无碰撞气体通过相空间中的速度弥散来容纳流交叉。我们为该情形发展了一个协变动力学框架，不假设背景时空或任何几何对称性。从精确的有质量Vlasov层级出发，我们构造其能量积分矩，并按速度权重进行组织。在四极处的一个自洽截断使动力学在物质能量密度、各向同性压强和各向异性压强上闭合。它们的梯度产生一个物质系中的4-加速度，我们为其找到了动量约束的一个精确非线性解，该解在一般情形下无需截断即有效。这超越了先前引入任意4-加速度的工作。速度弥散还通过4-加速度的旋度产生涡度，我们推导了涡度演化的非线性表达式。然后我们将非测地物质流传播到协变局部宇宙学中，其中4-加速度是固有的哈勃偶极，并进入减速多极。我们的构造提供了尘埃宇宙学的协变动力学补全，并确定了直接用局部距离-红移数据检验无碰撞物质所需的量。一篇配套论文将该层级特化到受扰动的FLRW时空，并预测了由此产生的宇宙学信号的幅度。
英文摘要
Modelling cold dark matter as dust makes the matter congruence geodesic and therefore removes any intrinsic dipole from the local Hubble flow. The dust model breaks down as stream crossing develops, whereas a collisionless gas accommodates stream crossing via velocity dispersion in phase space. We develop a covariant kinetic framework for this regime without assuming a background spacetime or any geometrical symmetry. Starting from the exact massive Vlasov hierarchy, we construct its energy-integrated moments and organise these by velocity weight. A self-consistent truncation at the quadrupole closes the dynamics on the matter energy density, isotropic pressure and anisotropic pressure. Their gradients generate a matter-frame 4-acceleration, for which we find an exact nonlinear solution of the momentum constraint, valid in the general case without truncation. This goes beyond previous work in which an arbitrary 4-acceleration is introduced. Velocity dispersion also sources vorticity through the curl of 4-acceleration, and we derive the nonlinear expression for vorticity evolution. We then propagate the non-geodesic matter flow into covariant local cosmography, where the 4-acceleration is the intrinsic Hubble dipole and also enters the deceleration multipoles. Our construction provides a covariant kinetic completion of dust cosmography and identifies the quantities required to test collisionless matter directly with local distance--redshift data. A companion paper specialises the hierarchy to perturbed FLRW spacetime and predicts the size of the resulting cosmographic signals.
Comments22 pages
