Modelling non-dust fluids in cosmology

TL;DR

This paper explores the limitations of Newtonian simulations in cosmology for fluids with pressure, providing a relativistic correction framework and analyzing scalar field dark matter as a case study.

Contribution

It establishes the exact correspondence between Newtonian and relativistic perturbations for pressureless matter and introduces relativistic corrections for fluids with pressure, such as scalar field dark matter.

Findings

Exact equivalence for pressureless matter

Relativistic corrections for pressure fluids

Potential issues in Newtonian simulations for scalar field dark matter

Abstract

Currently, most of the numerical simulations of structure formation use Newtonian gravity. When modelling pressureless dark matter, or `dust', this approach gives the correct results for scales much smaller than the cosmological horizon, but for scenarios in which the fluid has pressure this is no longer the case. In this article, we present the correspondence of perturbations in Newtonian and cosmological perturbation theory, showing exact mathematical equivalence for pressureless matter, and giving the relativistic corrections for matter with pressure. As an example, we study the case of scalar field dark matter which features non-zero pressure perturbations. We discuss some problems which may arise when evolving the perturbations in this model with Newtonian numerical simulations and with CMB Boltzmann codes.