We construct a consistency test of General Relativity (GR) on cosmological
scales. This test enables us to distinguish between the two alternatives to
explain the late-time accelerated expansion of the universe, that is, dark
energy models based on GR and modified gravity models without dark energy. We
derive the consistency relation in GR which is written only in terms of
observables - the Hubble parameter, the density perturbations, the peculiar
velocities and the lensing potential. The breakdown of this consistency
relation implies that the Newton constant which governs large-scale structure
is different from that in the background cosmology, which is a typical feature
in modified gravity models. We propose a method to perform this test by
reconstructing the weak lensing spectrum from measured density perturbations
and peculiar velocities. This reconstruction relies on Poisson's equation in GR
to convert the density perturbations to the lensing potential. Hence any
inconsistency between the reconstructed lensing spectrum and the measured
lensing spectrum indicates the failure of GR on cosmological scales. The
difficulties in performing this test using actual observations are discussed.Comment: 7 pages, 1 figur
