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.
