Dark energy homogeneity in general relativity: Are we applying it correctly?

TL;DR

This paper proposes a precise definition of homogeneous dark energy based on density perturbations in the comoving gauge, and explores its observational implications for galaxy power spectra, especially on large scales.

Contribution

It introduces a rigorous criterion for dark energy homogeneity and analyzes its effects on galaxy power spectrum measurements, highlighting potential observational distinctions.

Findings

Relativistic corrections can differentiate models on super-horizon scales.

Homogeneous DE must have zero density perturbation in the comoving gauge.

High magnification bias enhances the detectability of relativistic effects.

Abstract

Thus far, there does not appear to be an agreed (or adequate) definition of homogeneous dark energy (DE). This paper seeks to define a valid, adequate homogeneity condition for DE. Firstly, it is shown that as long as $w_x \neq -1$, DE must have perturbations. It is then argued, independent of $w_x$, that a correct definition of homogeneous DE is one whose density perturbation vanishes in comoving gauge: and hence, in the DE rest frame. Using phenomenological DE, the consequence of this approach is then investigated in the observed galaxy power spectrum - with the power spectrum being normalized on small scales, at the present epoch z = 0. It is found that for high magnification bias, relativistic corrections in the galaxy power spectrum are able to distinguish the concordance model from both a homogeneous DE and a clustering DE - on super-horizon scales.