标题： 随机暗物质：普朗克离散性的协变布朗运动 显示英文标题

标题： Stochastic dark matter: Covariant Brownian motion from Planckian discreteness

摘要： 量子引力长期以来从观测的角度来看一直难以捉摸。 开发由量子引力基本方面激发的有效宇宙学模型对于连接理论与观测至关重要。 一个关键方面是时空的粒度性，这表明自由粒子会偏离经典测地线，遵循协变布朗运动。 这种观点在因果集理论中的转向模型中得到了进一步支持，因果集是一种离散的量子引力方法。 在有效层面上，这种偏离由测地线方程的一个随机修正来描述。 我们证明了这种修正的形式严格受到协变性和质量壳条件的限制。 在最小曲率耦合下，由此产生的协变布朗运动是唯一的。 该过程可以通过相对论相空间中大质量粒子分布的协变扩散方程来等效描述。 当应用于暗物质粒子时，协变布朗运动会导致晚期自发升温，在时间依赖的方式下抑制小尺度上的物质功率谱。 利用来自 CMB 和 $f\sigma_8$ 的扩散速率约束以及增长历史测量结果，我们表明该模型解决了 $S_8$ 的张力。 未来对该模型在非线性宇宙尺度上的行为研究将提供进一步的限制，并因此对随机暗物质的可行性进行关键测试。 显示英文摘要

摘要： Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is the granularity of spacetime, which suggests that free particles would deviate from classical geodesics by following a covariant Brownian motion. This notion is further supported by swerves models in causal set theory, a discrete approach to quantum gravity. At an effective level, such deviations are described by a stochastic correction to the geodesic equation. We show that the form of this correction is strictly restricted by covariance and the mass-shell condition. Under minimal coupling to curvature, the resulting covariant Brownian motion is unique. The process is equivalently described by a covariant diffusion equation for the distribution of massive particles in their relativistic phase space. When applied to dark matter particles, covariant Brownian motion results in spontaneous warming at late times, suppressing the matter power spectrum at small scales in a time-dependent manner. Using bounds on the diffusion rate from CMB and growth history measurements of $f\sigma_8$, we show that the model offers a resolution to the $S_8$ tension. Future studies on the model's behavior at non-linear cosmological scales will provide further constraints and, therefore, critical tests for the viability of stochastic dark matter.