Gauge conditions in combined dark energy and dark matter systems

TL;DR

Neglecting dark energy perturbations in combined dark matter and dark energy systems implicitly chooses a gauge, which can lead to erroneous results if not properly accounted for, as shown through cosmological perturbation theory.

Contribution

This work clarifies the gauge dependence of neglecting dark energy perturbations and provides a formalism to avoid gauge-related errors without complex simulations.

Findings

Neglecting dark energy perturbations is equivalent to fixing a gauge.

Incorrect gauge choices lead to gauge-dependent and erroneous results.

Using cosmological perturbation theory ensures consistent analysis without numerical simulations.

Abstract

When analysing a system consisting of both dark matter and dark energy, an often used practice in the literature is to neglect the perturbations in the dark energy component. However, it has recently been argued, through the use of numerical simulations, that one cannot do so. In this work we show that by neglecting such perturbations one is implicitly making a choice of gauge. As such, one no longer has the freedom to choose, for example, a gauge comoving with the dark matter -- in fact doing so will give erroneous, gauge dependent results. We obtain results consistent with the numerical simulations by using the formalism of cosmological perturbation theory, and thus without resorting to involved numerical calculations.