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

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.

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