A null test to probe the scale dependence of the growth of structure as a test of general relativity

Abstract

The main science driver for the coming generation of cosmological surveys is understanding dark energy that 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 that 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.