  The main science driver for the coming generation of cosmological surveys is
understanding dark energy which relies on testing General Relativity on the
largest scales. Once we move beyond the simplest explanation for dark energy of
a cosmological constant, the space of possible theories becomes both vast and
extremely hard to compute realistic observables. A key discriminator of a
cosmological constant, however, is that the growth of structure is
scale-invariant on large scales. By carefully weighting observables derived
from distributions of galaxies and a dipole pattern in their apparent sizes, we
construct a null test which vanishes for any model of gravity or dark energy
where the growth of structure is scale-independent. It relies only on very few
assumptions about cosmology, and does not require any modelling of the growth
of structure. We show that with a survey like DESI a scale-dependence of the
order of 10-20 percent can be detected at 3 sigma with the null test, which
will drop by a factor of 2 for a survey like the Square Kilometre Array. We
also show that the null test is very insensitive to typical uncertainties in
other cosmological parameters including massive neutrinos and scale-dependent
bias, making this a key null test for dark energy.
