Dark energy homogeneity in general relativity: Are we applying it correctly?
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 wx = −1, DE must
have perturbations. It is then argued, independent of wx , 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.