AI 中文总结
该论文是格点宇宙学专题系列第三篇，介绍膨胀背景下标量-规范-流体耦合系统的格点模拟方法，为$\mathcal{C}{\tt osmo}{\mathcal L}{\tt attice}~{\tt v3.0}$的对应模块提供理论基础。
AI 中文摘要
本文讨论用于模拟早期宇宙流体动力学的格点方法，是关于格点宇宙学技术的专题系列第三篇，此前已涵盖正则与非正则场论动力学。首先回顾平直时空中流体动力学的连续理论，再介绍FLRW背景下的相关内容；研究流体运动方程的守恒与非守恒形式，包括孤立流体或与标量、规范场耦合的情况，以及流体整体运动的全相对论或亚相对论 regime。在回顾基础格点概念后，针对膨胀背景下的流体动力学引入详细离散格式，涵盖四类情况：i) 孤立理想流体、ii) 孤立非理想（粘性）流体、iii) 与规范场耦合的流体、iv) 与标量场耦合的流体。所提演化算法可适配所有标量、规范及流体部分源产生的自洽膨胀，部分场景下可将规范不变性保持至机器精度；还回顾了设置流体初始条件的格点方法，以及由所有标量、规范、流体自由度源产生的引力波动力学的实现方式。本文构成将作为$\mathcal{C}{\tt osmo}{\mathcal L}{\tt attice}~{\tt v3.0}$的一部分公开发布的标量-规范-流体模块的理论基础，该模块将在本专题出版后上线，更新信息可查看该网址。
英文摘要
We discuss lattice methods for the simulation of fluid dynamics in the early Universe. This review represents a third entry in the monographic series on lattice cosmology techniques~\cite{Figueroa:2020rrl,Baeza-Ballesteros:2025tme}, which previously covered canonical and non-canonical field theory dynamics. Here, we first review the continuum theory of fluid dynamics in flat spacetime, and then in an FLRW background. We consider conservation and non-conservation forms of the equations of motion for fluids in isolation or coupled to scalar and/or gauge fields, and either fully relativistic or subrelativistic regimes of fluid bulk motion. After reviewing basic lattice concepts, we introduce detailed discretization schemes for fluid dynamics in expanding backgrounds for: $i)$ isolated perfect fluids, $ii)$ isolated imperfect (viscous) fluids, $iii)$ fluids coupled to gauge fields, and $iv)$ fluids coupled to scalar fields. Our evolution algorithms accommodate self-consistent expansion sourced by all scalar, gauge, and fluid sectors, preserving gauge invariance to machine precision in some cases. We also review lattice methods to set up the initial conditions for fluids, and the implementation of gravitational wave dynamics sourced by all scalar, gauge, and fluid degrees of freedom. This document represents the theoretical basis for the scalar-gauge-fluid module that will be publicly released as part of ${\mathcal C}{\tt osmo}{\mathcal L}{\tt attice}~{\tt v3.0}$ after publication of this monograph, check http://www.cosmolattice.com for updates.
Comments78 pages, 2 appendices
