  The strongest evidence for dark energy comes presently from geometric
techniques such as the supernova distance-redshift relation. By combining the
measured expansion history with the Friedmann equation one determines the
energy density and its time evolution, hence the equation of state of dark
energy. Because these methods rely on the Friedmann equation which has not been
independently tested it is desirable to find alternative methods that work for
both general relativity and other theories of gravity.
  Assuming that sufficiently large patches of a perturbed Robertson-Walker
spacetime evolve like separate Robertson-Walker universes, that shear stress is
unimportant on large scales and that energy and momentum are locally conserved,
we derive several relations between long-wavelength metric and matter
perturbations. These relations include generalizations of the initial-value
constraints of general relativity. For a class of theories including general
relativity we reduce the long-wavelength metric, density, and velocity
potential perturbations to quadratures including curvature perturbations,
entropy perturbations, and the effects of nonzero background curvature. When
combined with the expansion history measured geometrically, the long-wavelength
solution provide a test that may distinguish modified gravity from other
explanations of dark energy.
