Non-linear Eulerian Hydrodynamics of Dark Energy: Riemann problem and Finite Volume Schemes

TL;DR

This paper develops numerical methods based on finite volume schemes and Riemann problem solutions to simulate inhomogeneous dark energy with non-zero sound speed, aiding future cosmological studies.

Contribution

It introduces a novel numerical framework for simulating dark energy perturbations using hydrodynamic methods and Riemann solvers.

Findings

Developed exact and approximate Riemann solvers for dark energy fluid

Constructed conservative finite volume schemes for cosmological simulations

Enabled modeling of inhomogeneous dark energy scenarios with small sound speed

Abstract

Upcoming large-scale-structure surveys can shed new light on the properties of dark energy. In particular, if dark energy is a dynamical component, it must have spatial perturbations. Their behaviour is regulated by the speed of sound parameter, which is currently unconstrained. In this work we present the numerical methods that will allow to perform cosmological simulations of inhomogeneous dark energy scenarios where the speed of sound is small and non-vanishing. We treat the dark energy component as an effective fluid and build upon established numerical methods for hydrodynamics to construct a numerical solution of the effective continuity and Euler equations. In particular, we develop conservative finite volume schemes that rely on the solution of the Riemann problem, which we provide here in both exact and approximate forms for the case of a dark energy fluid.