Probing Dark Energy through Scale Dependence
  We consider the consequences of having no prior knowledge of the true dark
energy model for the interpretation of cosmological observations. The magnitude
of redshift-space distortions and weak-lensing shear is determined by the
metric on the geodesics of which galaxies and light propagate. We show that,
given precise enough observations, we can use these data to completely
reconstruct the metric on our past lightcone and therefore to measure the
scale- and time-dependence of the anisotropic stress and the evolution of the
gravitational potentials in a model-independent manner. Since both dark matter
and dark energy affect the visible sector only through the gravitational field
they produce, they are inseparable without a model for dark energy: galaxy bias
cannot be measured and therefore the distribution of dark matter determined;
the peculiar velocity of dark matter can be identified with that of the
galaxies only when the equivalence principle holds. Given these limitations, we
show how one can nonetheless build tests for classes of dark energy models
which depend on making measurements at multiple scales at a particular
redshift. They are null tests on the model-independent observables, do not
require modeling evolution in time and do not require any parametrization of
the free functions of these models, such as the sound speed. We show how one
can rule out or constrain the whole class of the most-general scalar-tensor
theories even without assuming the quasi-static limit.
