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arXiv · 2607.27141

The art of simulating the early Universe. Part III: Scalar-Gauge-Fluid Dynamics

Daniel G. Figueroa·Kenneth Marschall·Antonino S. Midiri·Alberto Roper Pol
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Abstract

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.

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Daniel G. Figueroa, Kenneth Marschall, Antonino S. Midiri, Alberto Roper Pol. 2026-07-29. The art of simulating the early Universe. Part III: Scalar-Gauge-Fluid Dynamics. https://arxiv.org/abs/2607.27141

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